Pramodlna

Design And Implementation Of P- Band RF Low Noise Amplifier
CHAPTER 1

INTRODUCTION
Low-noise amplifier (LNA) is an electronic amplifier used to amplify possibly very
weak signals (for example, captured by an antenna) and it amplifies the signal while
introducing a minimum amount of noise. It is usually located very close to the
detection device to reduce losses in the feed line. This active antenna arrangement is
frequently used in microwave systems like GPS, because coaxial cable feed line is
very lossy at microwave frequencies, e.g. a loss of 10% coming from few meters of
cable would cause a 10% degradation of the signal-to-noise ratio (SNR).

1.1 Low Noise Amplifier
In comparison to other technologies, pHEMT is ideally, the two different materials
used for a heterojunction would have the same lattice constant (spacing between the
atoms). In practice, e.g. AlGaAs on GaAs, the lattice constants are typically slightly
different, resulting in crystal defects. As an analogy, imagine pushing together two
plastic combs with a slightly different spacing. At regular intervals, you'll see two
teeth clump together. In semiconductors, these discontinuities form deep-level traps,
and greatly reduce device performance. A HEMT where this rule is violated is called
a pHEMT or pseudomorphic HEMT. This is achieved by using an extremely thin
layer of one of the materials – so thin that the crystal lattice simply stretches to fit the
other material. This technique allows the construction of transistors with larger
bandgap differences than otherwise possible, giving them better performance is the
most cost-effective solution to date for large-scale digital applications and it enables
system-on-a-chip owing to its capability of providing large-scale subsystems with
high levels of integration. A number of fully integrated transceivers, up to 5GHz, are
being implemented using standard processes; typical protocols are Bluetooth, IEEE
802.11, IEEE 802.15.3, IEEE 802.11a, and Hipper- LAN. Nevertheless, the real
design of RF circuits is still a challenge due to severe constraints on power
consumption and noise that impose stringent margins to the design process. Accurate
models are critical in order to reduce design cycles and to achieve first - time success
in implementation. Unfortunately, available MOSFET compact models – such as

Centre for Emerging Technology, Jain University

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BSIM3v3, PHEMT Model, or EKV are typically not applicable for the GHz range of
frequencies. Modeling of noise provides critical information in the design of RF
circuits, especially for LNA (low noise amplifier) blocks.

The LNA is typically the first stage of a radio receiver and needs to provide sufficient
gain while introducing the least noise possible. Since it is indispensable to understand
the physical phenomena of broadband noise and to incorporate this information into
the models, lack of understanding of MOSFET noise presents a substantial barrier to
the implementation of CMOS receivers.

WIRELESS COMMUNICATIONS has thrived in the last decade, owing to exploding
user demand for information and the commensurate need for connectivity. Substantial
research effort has focused on many application areas, such as cellular phones,
cordless phones, GPS (global positioning system), and WLANs (wireless local area
networks). The RF ICs (radio frequency integrated circuits) have been the primary
domain of GaAs or bipolar technologies since those technologies provide relatively
high cutoff frequencies (fT). However, as continuous scaling of PHEMT makes fTin
excess of 30GHz readily achievable in typical quarter micron technology, PHEMT
becomes an attractive alternative for RF applications in the low GHz frequency range.

An LNA in a Heterodyne Receiver

Figure1.1: LNA used in a Super-heterodyne receiver.

The band-select filter before the LNA rejects the out-of-band interferers. The image
reject filter (preselected) after the LNA attenuates the image which is IF away from
the desired band. LNA design is a compromise among power, noise, linearity, gain,
stability, input and output matching, and dynamic range. They are characterized by
the design specifications.


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The first stage of a receiver is typically a low-noise amplifier (LNA), whose main
function is to provide enough gain to overcome the noise of subsequent stages (for
example, in the mixer or IF amplifier). Aside from providing enough gain while
adding as little noise as possible, an LNA should accommodate large signals without
distortion, offer a large dynamic range, and present good matching to its input and
output, which is extremely important if a passive band select filter and image-reject
filter precedes and succeeds the LNA, since the transfer characteristics of many filters
are quite sensitive to the quality of the termination.

An LNA combines a low noise figure, reasonable gain, and stability without
oscillation over entire useful frequency range.

GAIN

The gain G is defined as the ratio of the power delivered to the output to the power
available from the input. The greater the gain, the more the signal is amplified in the
amplifier. Gain is usually expressed in decibels (dB).

NOISE FIGURE

Every amplifier amplifies both the signal and the noise delivered to the input. Since
an amplifier is never ideal, it also adds some self-noise during the amplifying process
and therefore in the amplifier output there is a sum of amplified input noise and
amplifier self-noise in addition to the amplified signal. Thus, the signal-to-noise
ration always decreases between amplifier input and output. This decrease is
expressed by noise figure (NF) and is calculated in decibels.

INPUT AND OUTPUT MATCHING

The input and output are each connected to the LNA with filters whose performance
relies heavily on the terminal impedance. Furthermore, input and output matching to
the source and load can maximize the gain. Input and output impedance matching is
characterized by the input and output return loss.

STABILITY

Stability is an issue in all amplifiers with feedback, whether that feedback is added
intentionally or results unintentionally. It is especially an issue when applied ov er
multiple amplifying stages. Stability is a major concern in RF and microwave


3

amplifiers. The degree of an amplifier's stability can be quantified by a so-called
stability factor.

LINEARITY

An ideal amplifier would be a totally linear device, but real amplifiers are only linear
within limits. When the signal drive to the amplifier is increased, the output also
increases until a point is reached where some part of the amplifier becomes saturated
and cannot produce any more output; this is called clipping, and results in distortion.

Dealing with low frequency AC and DC circuits, conventional Kirchoff's voltage and
current laws are used as analysis tools. Heading into higher operating frequencies
those laws can no longer be applied without losing too much precision. Analyzing a
low frequency circuit, a conductor between two elements always assumes to have the
same potential regardless where on the conductor one looks. When it comes to higher
frequencies than around 500 MHz the previous assumption may no longer be correct.
The reason for this is that the wavelength of the signal becomes so small that voltage
and current will propagate as waves and therefore magnitude and phase vary along the
conductor.

Instead of using Kirchhoff's laws one must deal with electromagnetic waves and
issues like propagation constant β, phase velocity Vp and skin depth δ become
important. The propagation constant and phase velocity highly depend on the medium
surrounding the conductor and they will determine the wavelength for a specific
frequency. Since the surrounding medium is a crucial design parameter, choosing a
good substrate is one of the first design steps in RF-design. Skin effect is a
consequence that also occurs due to the electromagnetic wave nature and this effect
forces the majority of the energy to flow close to the surface of the conductor.
Penetration of the signal into the conductor is measured in skin depth δ. When the
energy is focused in just a few percent of the conductor the result is a decrease in
effective cross-sectional area. As a consequence, loss due to higher resistance will
occur. Changing the copper thickness will have little effect on trace resistance at high
frequencies, while changes in width and length will have the greatest effect on
resistance at high frequencies.


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1.2 PROJECT SCOPE AND METHODOLOGY
The Low Noise Amplifier (LNA) always operates in Class A, typically at 15 -20% of
its maximum useful current. Class A is characterized by a bias point more or less at
the center of maximum current and voltage capability of the device u sed, and by RF
current and voltages that are sufficiently small relative to the bias point that the bias
point does not shift.

The dynamic range of the receiver, the difference between the largest possible
received signal and the smallest possible received signal, defines the quality of the
receiver chain. The LNA function, play an important role in the receiver designs. Its
main function is to amplify extremely low signals without adding noise, thus
preserving the required Signal-to-Noise Ratio (SNR) of the system at extremely low
power levels. Additionally, for large signal levels, the LNA amplifies the received
signal without introducing any distortions, which eliminates channel interference.

 An LNA design presents a considerable challenge because of its simultaneous
requirement for high gain, low noise figure, good input and output matching
and unconditional stability at the lowest possible current draw from the
amplifier.

 Although Gain, Noise Figure, Stability, Linearity and input and output match
are all equally important, they are interdependent and do not always work in
each other‘s favor.

 Carefully selecting a transistor and understanding parameter trade-offs can
meet most of these conditions.

 Low noise figure and good input match is really simultaneously obtained
without using feedback arrangements.

 Unconditional stability will always require a certain gain reduction because of
either shunt or series resistive loading.Transistor selection is the first and most
important step in an LNA design.

The smallest signal that can be received by a receiver defines the receiver sensitivity.
The largest signal can be received by a receiver establishes the upper power level
limit of what can be handled by the system while preserving voice or data quality.


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The designer should carefully review the transistor selection, keeping the most
important LNA design trade-offs in mind. The transistor should exhibit high gain,
have a low noise figure, and offer high IP3 performance at the lowest possible current
consumption, while preserving relatively easy matching at frequency of operation.
Examination of a data sheet is a good starting point in a transistor evaluation for LNA
design.

The transistor‘s S-parameters should be published at different source/drain voltages
and different current levels for frequencies ranging from low to high values. The data
sheet should also contain noise parameters, which are essential for low noise design.

The designer should first look at the main design parameters as: Noise, Gain and
decide what Vds and Ids levels will produce optimal performance.

The forward transducer power gain represents the gain from transistor itself with its
input and output presented with 50 Ω impedance, the manufacturer of the transistor at
multiple frequencies and different Vds and current levels provides the S21 values.
Additional gain can be obtained from source and load matching circuits. Maximum
Stable Gain and Maximum Power Gain (Gmax) are good indicators of additional
obtainable gain from the LNA circuit. LNA linearity is another important parameter.

In amplifier design, there are a number of design techniques available in the literature
depending on the parameter to be optimized. The most important design
considerations in a microwave amplifier design are stability, power gain, bandwidth,
and noise and DC requirements.

RF performance of the LNA depends by many variables as:

 Frequency

 Stability

 Input and Output Matching

 Layout and Grounding

 EM Shielding

 Supply decoupling

General procedure for microwave amplifier design


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Any MIC amplifier design essentially consists of the following steps.

1. Selection of a proper transistor.

2. Checking the conditional stability.

3. If transistor is unstable at the desired frequency, proper techniques are applied
to make it stable.

4. Biasing is done. Bias point is selected depending on the application like low
power, low noise, high power, linearity etc.

5. Different techniques are applied to optimize different parameters like noise
figure, gain, power dissipation. Two parameters cannot be optimized
simultaneously. Matching circuits that provide optimum performance in a
microwave amplifier can be easily and quickly designed using a Smith chart.

1.3 AMPLIFIER SPECIFICATIONS

Parameters Required
Frequency range 50M-1GHz
Gain(min) 22dB(20dB)
Gain flatness +/- 1dB
Noise figure <4dB
Power output 26dBm
VSWR or return loss 1:2 input 1:2 output
All port imp 50Ω
Maximum RF input 10dBm
Supply Voltage 15V
Current, maximum 1000mA

1.3 THESIS ORGANIZATION
The thesis is organized as follows. Chapter 2 deals with Literature survey. In chapter
3 background theories, Chapter 4 deals with system design i.e., stability design and
matching circuit design. The design implementation is discussed in chapter 5. Chapter
6 discusses the simulation results obtained and chapter 7 concludes the thesis work.


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CHAPTER 2

LITERATURE SURVEY
In wireless receiver modules, the ability of LNA to meet the objective of providing
sufficient amplification for subsequent stages while adding as little noise as possible
is quantified in the noise factor of the amplifier which is defined as the ratios of the
signal-to-noise ratio at the output of the amplifier to the signal-to-noise ratio at the
input. It is well known that the first amplification stage dominates the total noise
figure of the system and thus the noise optimization of this first stage is critical. In the
absence of LNA, the received signal will be very weak. It cannot be processed by the
next stage. In general the important characteristics of LNA are: high Gain, low Noise
figure, Stability, Linearity and good input output matching

An ideal amplifier would be a totally linear device, but real amplifiers are only linear
within limits. When the signal drive to the amplifier is increased, the output also
increases until a point is reached where some part of the amplifier becomes saturated
and cannot produce any more output; this is called clipping, and results in distortion.

As the applications move towards frequencies then new design challenges are
introduced. At high frequencies, the noise performances of silicon bipolar junction
transistors (BJT) are no longer satisfactory. Traditionally III-V compounds such as
GaAs or lnP were used in high-speed applications, as they are capable of achieving
high unity gain frequencies, efficiency and low voltage.

The HEMT or High Electron Mobility Transistor is a form of field effect transistor
(FET) that is used to provide very high levels of performance at microwave
frequencies. It offers a combination of low noise figure combined with the ability to
operate at the very high microwave frequencies. Accordingly the HEMT is used in
areas of RF design where high performance is required at very high RF frequencies.

The development of the HEMT took many years. It was not until many years after the
basic FET was established as a standard electronics component that the HEMT
appeared on the market. The specific mode of carrier transport used in HEMTs was
first investigated in 1969, but it was not until 1980 that the first experimental device s
were available for the latest RF design projects. During the 1980s they started to be


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used, but in view of their initial very high cost their use was considerably limited.
Now with their cost somewhat less, they are more widely used, even finding uses in
the mobile telecommunications as well as a variety of microwave radio
communications links, and many other RF design applications.

Figure 1.2 cross sectional schematic of HEMT

High Mobility Electron Transistors (HEMTs) outperform MESFETs in noise figure,
output power and high frequency operations.

Heterojunction HEMT replaces Schottky barrier in MESFET Superior electron
transport properties due to formation of two-Dimensional electron gas (2DEG)

 High mobility.

 High transconductance.

 Ultra low noise.

A further development of the HEMT is known as the PHEMT. PHEMTs,
Pseudomorphic High Electron Mobility Transistors are extensively used in wireless
communications and LNA applications. PHEMT transistors find wide market
acceptance because of their high power added efficiencies and excellent low noise
figures and performance. As a result, PHEMTs are widely used in satellite
communication systems of all forms including direct broadcast satellite television,
DBS-TV, where they are used in the low noise boxes, LNBs used with the satellite
antennas. They are also widely used in general satellite communication systems as
well as radar and microwave radio communications systems. PHEMT technology is


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also used in high-speed analogue and digital IC technology where exceedingly high
speed is required.

It has been shown that the input impedance matching plays an important role in
achieving minimum noise figures and that an optimal source impedance exists for
achieving the best noise performance. This impedance is usually different than for
maximum power transfer.LNA design entails achieving a low noise figure and usually
optimal noise matching for a first amplifier stage. The obvious trade-off between
minimum noise and maximum available gain has sparked much research interest into
achieving a simultaneous optimal noise and power match. A traditional approach is
the shunt-shunt feedback to modify the amplifier input impedance achieving such a
simultaneous match.

In 1995[4], A methodology which permits one to determine the required input and
output termination impedances of a given transistor such that the amplifier can
simultaneously meet power gain, noise figure, and input and output VSWR constraints
is described. To support the proposed method, an amplifier design example at 2 GHz
with power gain, noise figure, and input and output VSWR constraints is presented.
The applicability of the design methodology to the design of broad band low-noise
amplifier design is demonstrated with three examples.

In 2003[5], A low-noise amplifier (LNA) uses low-loss monolithic transformer
feedback to neutralize the gate–drain overlap capacitance of a field-effect transistor
(FET). A differential implementation in 0.18- m CMOS technology, designed for 5-
GHz wireless local-area networks (LANs), achieves a measured power gain of14.2
dB, noise figure (NF, 50 ) of 0.9 dB, and third-order input intercept point (IIP3) of
+0.9 dBm at 5.75 GHz, while consuming16 mW from a 1-V supply. The feedback
design is bench marked to a 5.75-GHz cascade LNA fabricated in the same
technology that realizes 14.1-dB gain, 1.8-dB NF, and IIP3 of+4.2 dBm, while
dissipating21.6 mW at 1.8 V.

In 2007[7], various design methodologies for common-source low noise amplifiers
(LNAs) in Si CMOS technologies were proposed in the past. These starts from long-
channel assumptions to derive analytic design equations. This paper compares the
various existing LNA design methodologies and verifies the long-channel


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assumptions using a commercial .13μm CMOS technology. After demonstrating that
the design assumptions are no longer valid, a new methodology is proposed which
enables the LNA design in a systematic way, without the drawback that it is relying
on a particular transistor model for computing the input impedance and the noise
figure. This makes the proposed technique robust to transistor model changes in
future technology nodes.

In 2008[6], A narrowband LNA is designed at the center frequency of 12.7GHz with a
gain of 10dB, bandwidth of 72MHz and noise figure of 3 to 4dB. The design
methodology required the analysis of the transistor, stability check and proper
matching network selection for input and output. Ideal microwave amplifier equations
are used to carry out the analytical treatment for the design. The DC and AC
simulations for the LNA are presented in the paper. Fabrication and testing of the
LNA is also discussed.

In 2009[8], In this paper the aim is to design and simulate a single stage LNA circuit
with high gain and low noise using MESFET for frequency range of 5 GHz to 6 GHz.
A single stage LNA has successfully designed with15.83 dB forward gain and 1.26 dB
noise figure in frequency of 5.3GHz. Also the designed LNA should be working
stably in a frequency range of 5 GHz to 6 GHz .

In 2009[9], an integrated narrowband low noise amplifier in cascade topology has
been developed for WLAN applications. Using WIN's 0.15μm PHEMT technology,
the impedance matching, voltage gain, noise figure and 1dB compression point of the
circuit are analyzed and optimized under specified power consumption. Results from
the simulation show that the maximum forward gain of the circuit is 20dB, noise
figure is 0.93dB, OP1dBis 10dBm at the center frequency of 2.4GHz, while
consuming42mA current from a 3.3V power supply.

In 2011[10], the design of a compact, two-stage, low noise, unconditionally stable,
amplifier from 0.5 to 6 GHz is discussed. To achieve its wide-band characteristics, a
novel matching mechanism is proposed, which consists of lumped elements and
micro-strip lines. The amplifier is designed around the HEMT FHX35LG and the
PHEMT ATF-54143. The negative feedback technique is also adapted to border the
frequency band, and the whole matching network. In the covered band, the amplifier


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provides more than 22 dB gain, gain-flatness of less than ±2 dB, noise figure of less
than 4 dB, linear output power (P -1dB) of more than 26 dBm.

In 2012[11], a very low noise LNA is designed. The LNA is based on reactive
feedback and the broadband impedance matching and the flat gain are achieved. Also
by using inductive degeneration, a noise less resistance is created. This impedance is
used to match the input impedance without increasing the noise figure. The LNA is
designed in the standard 0.18 μm CMOS technology. The noise figure (NF) is
below0.8dB and input and output reflection coefficient are less than -10dB.Also LNA
provides 12dB power gain and consume 11.9mW from a1.2-V voltage supply.

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12

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High Electron Mobility Transistors (HEMTs)

 Heterojunction Structure

 Energy Bands

 Two-dimensional Electron Gas (2DEG)

PHEMT for cryogenic low-noise amplifications recent development:

State-of-the-art LNAs in Radio Astronomy Receivers

In a PHEMT, conduction electrons are spatially separated from the donor impurities
ionized scattering is suppressed Electrons in a 2DEG exhibit very high mobility

High Gain: High electron mobility leads to high transconductance gm and high
operation frequency (millimeter wavelengths)

Low-noise: Superior noise temperatures, especially In-P based HEMTs for low noise
and power amplifications; p-HEMT is generally recognized as the best choice.

 InP-HEMTs are promising in better gain and noise, but still await
commercialization

 Amplification up to 40GHz: GaAs-HEMTs and p-HEMTs.

 Above 40GHz: InP-based HEMTs .

 100GHz –1 THz: Superconductor-insulator- superconductor (SIS) junction
devices.

 Above 1THz: Hot electron bolo meters (HEB).


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CHAPTER 3

BACKGROUND THEORY
For a fundamental understanding of the Low-Noise Amplifier design procedure, it is
necessary to introduce a series of underlying concepts. Covered topics include
reflection, scattering p a r a m e t e r s , the Smith Chart, t h e quality factor, and
impedance transformation.

3.1 Scattering Parameters
Scattering Parameters or S-parameters are complex numbers that exhibit how voltage
waves propagate in the radio-frequency (RF) environment. In matrix form they
characterize the complete RF behavior of a network.

At this point it is necessary to introduce the concept of 2-ports. It is fundamental in
RF circuit analysis and simulation as it enables representation of networks by a single
device. As the properties of the individual components and those of the physical
structure of the circuit are effectively taken out of the equation, circuit analysis is
greatly simplified. The characteristics of the 2-port is represented by a set of four S-
parameters: S11, S12, S21 and S22, which correspond to input reflection coefficient,
reverse gain coefficient, forward gain coefficient and output reflection coefficient
respectively.

√

√

√

√

Figure 3.1(a): Two port network

There are alternative descriptive parameters for 2-ports, such as impedance
parameters, admittance parameters, chain parameters and hybrid parameters. These
are all measured on the basis of short-and open circuit tests, which are hard to carry


14

out accurately at high frequencies. S-parameters, on the other hand, are measured
under matched and mismatched conditions. This is why S-parameters are favored in
microwave applications. S-parameters are both frequency-and system impedance
dependent so although manufacturers typically supply S-parameter data with their
devices it is not always applicable. Under such circumstances, it becomes necessary to
measure the parameters. Referring to Figure3.1 (a), these measurements are carried
out by measuring wave ratios while systematically altering the termination to cance l
either forward gain or reverse gain according to the following equations:

A two-port network is inserted between source and load, which is shown in the circuit
of Figure 3.1(a). The following may be said for any traveling wave that originates at
the source:

A portion of the wave that originates at the source and is incident on the two -port
device (a1) will be reflected (b1), and another portion will be transmitted through the
two-port device.

A fraction of the transmitted signal is then reflected from the load and becomes
incident on the output port of the two-port device (a2).A portion of the signal (a2) is
then reflected from the output port back toward the load (b2), while a fraction is
transmitted through the two-port device to the source.

Figure 3.1(b): Two port network

It is obvious from the above discussion that any traveling wave present in the circuit
is composed of two components. For instance, the traveling wave components flowing
from the output of the two-port device to the load consist of the portion of a2 reflected
from the output of the two-port device, and the portion of a1 transmitted through the
two-port device. Similarly, the traveling wave flowing from the input of the two -port
device back toward the source consists of the portion of a1 reflected from the input
and the fraction of a2 transmitted through the two-port device.


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If we set these observations in equation form we get the following:

(3.1)
(3.2)

The above equations in the matrix form can be written as given below in the equation

[ ] [ ]* + (3.3)

From the Equation 3.3, the parameters S11, S12, S21 and S22 which represent
reflection and transmission coefficients, are called Scattering-parameters of the two
port network and are measured at port 1 and port 2. The matrix for these parameters
is;

[ ] (3.4)

From Figure 3.1, The Scattering-parameters measured at the specific locations are
defined as follows

Where:
S11 =the input reflection coefficient.
S12 = the reverse transmission coefficient.
S21 = the forward transmission coefficient.
S22 = the output reflection coefficient.
a1, a2 = Normalized incident voltage wave traveling towards the two-port network
b1, b2 = Normalized Reflected voltage wave reflected back from the two-port network

3.2 Reflection
When a wave travels through an impedance discontinuity, at that junction (Figure 3.1),
a fraction of the wave will be reflected. As a consequence, the counterpart (the


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incident wave) will lose some of its magnitude. Naturally, this is an undesirable
phenomenon in any application where power conservation is critical. The extent of
incident power loss is related to the similarity of the impedances as seen in both
directions from the junction. So the objective, In order to maximize the power
transfer, is to optimize the impedance match. Further information on that subject
follows in Chapter 3.

There are a number of performance parameters that‘s how to what extent the
impedances are matched. Firstly, the Reflection Coefficient which by definition is the
ratio of the reflected wave to the incident wave (Equation 3.5), but can also is
expressed in terms of impedances. It is a complex entity that describes not only the
magnitude of the reflection, but also the phase shift.

Note that this is the load reflection coefficient with respect to the source impedance. It
is also commonly expressed with respect to the characteristic impedance (Z0 ). When
the load is short-circuited, maximum negative reflection occurs and the reflection
coefficient assumes minus unity. In contrast, when the load is open-circuited,
maximum positive

Figure 3.2: Simple circuit showing the impedance discontinuity junction and
measurement location of Γ L.

Reflection occurs and the reflection coefficient assumes plus unity. In the ideal case,
when Z Lis perfectly matched to ZS, there is no reflection and the reflection coefficient
is consequently zero.

A closely related parameter is the Voltage Standing Wave Ratio (VSWR), which is
commonly talked about in transmission line applications. As the incident and
reflected wave travel in opposite directions the addition of the two generates a
standing wave, see Figure 3.2. The VSWR is defined as the ratio of the maximum
voltage to the adjacent minimum voltage of that standing wave (Equation
3.8).Knowing the domain of the reflection coefficient, it follows that when there is no


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reflection as in a perfectly matched system; VSWR assumes its minimum and ideal
value of 1.0:1.

The Return Loss (RL) is simply the magnitude of the reflection coefficient in decibels

3.3 The Smith Chart
By using the smith chart, RF circuit problems including noise factor optimization,
stability analysis and impedance matching circuits etc can be found. Among all the
RF circuit problems above, designing of impedance matching circuits is very hard and
important.

Figure 3.3: the complete Smith Chart

The center point in Smith chart represents normalized impedance Z = 50 Ώ which is
the load in case of perfectly matched circuit. At the extreme left side of smith chart


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there is a point represents short circuit that means Z = 0 Ώ and the in extreme right
side there is one point which represents open circuit it means Z = ∞ Ώ . Points
elsewhere on unity circle represents pure resistance values and points on arcs will
represents reactance values.

In its most common form, the chart is made up out of two overlaid grids: the constant
resistance circles and the constant reactance circles. The Cartesian coordinate system
within the Smith Chart is used to plot the reflection coefficient. Further more there
are three varieties of the Smith Chart: with impedance grid (Z Smith Chart), with
admittance grid(Y Smith Chart) and the two combined (ZY Smith Chart).As the
radius of the chart is unity, it is implied that all plotted values, whether they are
impedances or admittances, must be normalized with respect to a reference. This
reference is usually the characteristic impedance of the system which usually is 50Ω.
In impedance chart all circles are started from the right side. A large circle means
decreasing resistance and it is noted as R. It does not matter where you are on the
same circle; always resistance value is same on this circle. There is another reactance
curve in the smith chart which starts from the right hand side and stretch out like
increasing arcs is the reactance (jx).the bigger the arch is the smaller the reactance
value.

The impedance chart is shown in the below figure

Figure 3.4: Constant Resistance Circles

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The admittance chart is shown in the below figure 3.7.

Figure 3.5: Constant Reactance and suceptance Circles

Along the horizontal line in the middle, the reactance is always zero because there is
only resistive part. (R = 0).At this horizontal line end of the right side is open (R = ∞)
and the left side circuit is shorted (R = 0). Admittance chart (Y) is just like
impedance. It is simply inverse of Z (Y = 1/Z) .graphically it is possible by rotating
the smith chart 180 degree around.


20

Figure 3.6: Combination of Z and Y Smith Chart

An impedance value can also be turned 180 degree around to find the admittance
value. When both impedance and admittance chart shows in one figure than it is
called normalized impedance and admittance coordinates smith chart. It is often
referred to as a ZY smith chart. Figure 3.8 shows the combination of impedance and
admittance smith chart.

Admittance chart contains both real and imaginary part same as impedance has

Y = G±jB.

Where

G = Conductance

B = Susceptance

Many sources and loads have values greater than 50-ohm (ZS = 50+j100, ZL =
100+j100).The smith chart cannot represent this value so the smith chart shows
normalized impedance values. To transform to a normalized value first we have to
know the characteristic impedance value Z0 (50 Ohm, 75 Ohm) then simply divided
the actual value of ZS or ZL with characteristic impedance Z0 i.e. z = ZS/Z0 or z =
ZL/Z0.

3.4 The Quality Factor
The Quality Factor (Q)is a descriptive parameter of the rate of energy loss in complete
RLC networks or simply individual inductors or capacitors. For the latter, Q is a
measurement of how lossy the component is, that is how much parasitic resistance
there is. So it follows that in applications where loss is undesirable, high Q
components are advantageous. Additionally the Q factor is directly related to the
bandwidth, where higher corresponds to narrower bandwidth. The equations for
calculating Q are:

(3.9)

(3.10)

(3.11)


21

(3.12)

3.5 Impedance Transformation
As previously stated, in order to maximize power transfer from source to load,
matching impedances is required. Specifically, in a circuit as seen in Figure3.1 where
the source and load impedances are fixed, the objective is to design the input
matching network so that ZS matches Z1 and the output matching network so that
ZL matches Z2. In other words Z1 and Z2 respectively, are transformed to
perceptually match the input and output impedances of the transistor.

Figure 3.7: Different Direction of movements on Smith Chart and the
corresponding elements.

According to the Maximum Power Theorem, the maximum power transfer will occur
when the reactive components of the impedances cancel each other, that is when they
are complex conjugates. This is suitably called conjugate matching.

To achieve the conversion with an impedance matching network of passive
components, there are primarily three options. Firstly, there is the L-match .Its


22

advantage is the simplicity, but that is simultaneously its down side as well because it
has only two degrees of freedom. Since there are only two component values to set,
the L-match is restricted to determining only two out of the three associated
parameters: impedance transformation ratio, centre frequency and Q. To acquire a
third degree of freedom, it is therefore desired to cascade another L-match stage. By
doing so, another two types of impedance transformation matches are encountered:
the π-match and the T-match.

The above figure 3.9 shows the different ways of placing the elements depending
upon the direction of movement on smith chart. The advantages with the T-and π-
match configurations do not end with an additional degree of freedom. But because of
their topology they can absorb parasitic reactance present in source or load.
Specifically the T-match will absorb parasitic inductance where as the π-match will
absorb parasitic capacitance. In addition it is also possible to achieve significantly
higher Q compared to an L-match configuration.

3.6 Stability
When embarking on any amplifier design it is very important to check on the stability
of the device chosen, otherwise the amplifier may well turn into an oscillator. The
main way of determining the stability of a device is to calculate the Rollett‘s stabil ity
factor (K), which is calculated using a set of S-parameters for the device at the
frequency of operation.

The conditions of stability at a given frequency are |Γin| < 1 and |Γout| < 1,and must
hold for all possible values ΓL &ΓS obtained using passive matching circuits. We can
calculate two Stability parameters K & |∆| to give us an indication to whether a device
is likely to oscillate or not or whether it is conditionally/unconditionally stable.

Where

S11 = Input reflection coefficient


23

S22 = Output reflection coefficient

S12 = Reverse transmission gain

S21= Forward transmission gain

The parameters must satisfy K > 1 and |∆| < 1 for a transistor to be unconditionally
stable. Once we have calculated the K factor and find the device to be unconditionall y
stable we can calculate the Maximum available gain (MAG):-

Where K is on the limit of unity the above equation reduces down to:-

( √ ) (3.14)

(3.15)

The equations for calculation of the stability circles are:-

(3.16)

This gives the location of the centre of the input stability circle

.This gives the radius of the input stability circle.

| | (3.17)

Similarly for the output

This gives the location of the centre of the output stability circle

(3.18)

(3.19)

| | (3.20)

This gives the radius of the output stability circle.

The Figure below shows the form of stability circles in relation to a Smith chart.

In the above example the active device would be showing unconditional stability, as
there is no intersection of the stability circles on the Smith Chart. All devices with
S11 and S22 < 1 must be stable with a load impedance of 50 ohms therefore; the

24

centre of the Smith chart must always be a stable region. In the above example the
device will be stable for all possible matches on the input or output of the active
device.

Figure 3.8 stability circles.

However, in the case where S11 or S22 > 1 and the stability circle cover the centre of
the Smith chart then this region is unstable the following diagram shows the regions
of instability.

The Figure below (Figure 3.9) shows the areas of instability with S11 <> 1 & S22<1.

Figure 3.9 Areas of instability

25

Calculations of stability circles are tedious, prone to error and in addition they should
be plotted across a range of frequencies – low frequency to at least the ft of the active
device. This because a match may be clears of a region of instability at the pass-band
frequencies but may be in a region of instability at another out of band frequency. A
common problem of FET devices is that they are conditionally stable and have the
stability circles clipping the outer edge of the Smith chart. This means that if an open
or short circuit is applied to the input then the device may well oscillate. This may not
be a problem where a broadband load is applied but in case of antennas for example
they often are open/short circuit at very low frequencies and together with the very
high gain of the active device at low frequencies often leads to oscillation.

As shown in figure 3.12 there is still some potential instability with applied high
impedance at around 10GHz. However the resulting matching circuit will have some
loss at this frequency so the impedance at this frequency will always be lower.

.

Figure 3.10 shows several methods of stabilization

If when the circuit is re-simulated with RF bias networks and matching applied, there
is some additional stabilizing (a) is the addition of a series resistor to ensure that no
match is capable of intersecting an input stability circle to tend to clip the outer edge
of the Smith chart. That is why some devices especially FET‘s readily oscillat e when
an open or short circuit is applied to the input of the device. A note of caution
however that is the addition of a resistor will greatly increase the noise figure of the
device as the resistor acts as a noise generator.

The second method (b) involves adding a fairly high value shunt resistor across the
output of the device. The DC block ensures that the DC bias to the drain/collector is
not upset.


26

The third method (c) involves the use of a quarter wavelength piece of transmission
line connected to a resistor usually 50 ohms. At the resonant frequency the quarter
wavelength transmission line being an open circuit at one end will be transformed to a
short circuit at the resistor end. Therefore, at the resonant frequency the resistor will
be effectively shorted to ground ensuring a 50ohm load to the device. This method is
generally required for high frequency problems with devices having very high Ft‘s.

Additionally 50-ohm resistors can be added to the bias networks to ensure that a 50-
ohm resistor is connected at low frequencies where the gain of the device is at its
highest.

3.7 Gains for Two-Port Networks
The ratio between the signal outputs of a system to signal input of a system is called
gain. For LNA design there are three power gain definitions appears in the literature.

 Transducer power gain (GT)

 Operating power gain (GP)

 Available power gain (GA)

3.7.1 Transducer Power Gain (GT)
The ratio of the power delivered to the load and the power available from the source is
called Transducer power gain. The equation for transducer power gain is given
below

GT = PPower delivered to the load / PPower available from the source.

The equation for transducer power gain is given below

3.7.2 Operating Power Gain (GP)
The ratio between powers delivered to the load and the power input to the network is
called Operational Power Gain.

Gp = PPower delivered to the load / PPower input to the network.

27

The equation for Operating Power Gain is given below

3.7.3 Available Power Gain (GA)
The ratio between the power available from the network and power from the source

GA = P Available form the network / PAvailable form the source

The equation of Available Power Gain is given below

Beside these three gain definitions, there are three additional gain definitions that can
be use for LNA design.

 · Maximum unilateral transducer power gain (Gumx)

 · Maximum transducer power gain (Gmax)

 · Maximum stability gain (Gmsg)

3.7.4 Maximum Unilateral Transducer Power Gain (Gumx)
Gumx is the transducer power gain with assumption of S12 to be zero and the sou rce-
load impedances are conjugate matched to the LNA, i.e. Gs = S*11 and GL = S*12.

3.7.5 Maximum Transducer Power Gain (Gmax)
Gmax is the simultaneous conjugate matching power gain , when input and output
both are conjugate matched.GS = G*in and GL = G*out when S12 is small and Gumx
is close to Gmax.

Where

K= Stability

( √ )


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3.7.6 Maximum Stability Gain (Gmsg)
Gmsg is the maximum of Gmax when stability k is greater than one is still satisfied. It
is defined as the ratio of magnitude of to the magnitude of .

3.8 Noise
Objects capable of allowing the flow of electrical current will exhibit noise. This
occurs as some electrons will have a random motion, causing fluctuating voltage and
currents. As noise is random it can only be predicted by statistical means, usually with
a Gaussian probability density Function as shown below:-

Figure 3.11 Gaussian probability density Function

As noise is random then it‘s mean value will be zero, hence we use mean square
values, which are measurements of the dissipated noise power. The effective noise
power of a source is measured in root mean square of rms values. Ie Vn=Vn2 (rms)

3.8.1 Noise power spectral density – describes the noise content in a 1Hz bandwidth.
Units are V2/Hz and denotes as Svn(f). The graph below shows how Svn(f) is defined.

3.8.2 Equivalent Noise Bandwidth (NBW) - is defined as the frequency span of a
noise power curve with an amplitude equal to the actual peak value, and with the
same integrated area. In other words the NBW describes the bandwidth of a ‗brick
wall‘ system with the same noise power as the actual system (f1 is set such that the
area of the ‗brick wall‘ is ~ equal to the whole function). The graph below shows a
couple of examples.


29


Figure 3.12 shows examples for whole functions

The main constituents of noise in a system, is due to Shot, Thermal, Burst, Avalanche
and Flicker noise.

3.8.3 Shot noise – This noise is generated by current flowing across a P-N junction
and is a function of the bias current and the electron charge. The impulse of charge q
depected as a single shot event in the time domain can be Fourier transformed into the
frequency domain as a wideband noise ie

Figure 3.13 shows shot noise in time and frequency domain

3.8.4 Thermal noise – In any object with electrical resistance the thermal fluctuations
of the electrons in the object will generate noise ie

vn2 = 4kTRV 2 / Hz Where k = Boltzmann' s constant (1.38x10 -23 J/K)

The spectral density of thermal noise is flat with frequency and is known as white
noise.

3.8.5 Burst noise – occurs in semiconductor devices, especially monolithic amplifiers
and manifests as a noise crackle.


30

3.8.6 Avalanche noise – occurs in Zener diodes are reversed biased P-N junctions at
breakdown. This noise is considerably larger than shot noise, so if zeners have to be
used as part of a bias circuit then they need to be RF decoupled.

3.8.7 Flicker noise – This noise occurs in almost all electronic devices at low
frequencies and takes the form of:-

Figure 3.14 shows Flicker noise frequency domain

Flicker noise is usually defined by the corner frequency FL.

Equivalent Noise Model

Figure 3.15 shows Equivalent noise model

When analyzing a circuit we transform the many possible sources of noise (generating
noise currents and voltages) to an equivalent noise source at the input of the circuit ie

3.8.8 Noise figure (NF) is a measure of degradation of the signal-to-noise
ratio (SNR), caused by components in a radio frequency (RF) signal chain. The noise
figure is thus the ratio of actual output noise to that which would remain if the device
itself did not introduce noise.

The noise factor of a system is defined as:

(3.27)


31

The noise figure is defined as:

NF=10log(F) (3.28)

The noise figure is the noise factor expressed in dB where and are also
in decibels (dB):

Where

NF= Noise figure

SNRin = Signal to Noise ratio at the input of a circuit or system

SNRout = Signal to Noise ratio of the circuit or system at output.

Or Noise Figure is simply defined by

(3.30)

There are three key parameters that are needed for the noise figure analysis of an RF
amplifier.

 Minimum noise figure NFmin, that depends on the biasing condition and operating

 Frequency of the device.

 Equivalent noise resistance Rn

 Optimum reflection coefficient Γopt

3.8.9 The Friis formula for noise factor

Friis's formula is used to calculate the total noise factor of a cascade of stages, each
with its own noise factor and gain. The total noise factor can then be used to calculate
the total noise figure. The total noise factor is given as

(3.31)

where and are the noise factor and available power gain, respectively, of the n-th
stage. Note that both magnitudes are expressed as ratios, not in decibels.

An important consequence of this formula is that the overall noise figure of a radio
receiver is primarily established by the noise figure of its first amplifying stage.
Subsequent stages have a diminishing effect on signal-to-noise ratio. For this reason,

32

the first stage amplifier in a receiver is often called the low-noise amplifier (LNA).
The overall receiver noise figure is then-

Where is the overall noise factor of the subsequent stages. According to the
equation, the overall noise figure is dominated by the noise figure of the
LNA, if the gain is sufficiently high.

3.8.10 The Friis formula for noise temperature

Friis's formula can be equivalently expressed in terms of noise temperature:

3.9 VSWR
The SWR is usually defined as a voltage ratio called the VSWR, for voltage standing
Wave ratio. For example, the VSWR value 1.2:1 denotes maximum standing wave
amplitude that is 1.2 times greater than the minimum standing wave value. It is also
possible to define the SWR in terms of current, resulting in the ISWR, which has the
same numerical value. The power standing wave ratio (PSWR) is defined as the
square of the VSWR.

The VSWR is related to the reflection coefficient as:

Where ρ = the magnitude of the reflection coefficient.

It is also defined as the superposition of forward travelling wave and reflected
travelling wave when the transmission line is terminated with other than its
characteristic impedance.

(3.35)

Where Γ is the reflection coefficient which is the ratio of reflected wave to the
forward wave.


33

The way to improve VSWR of the system is to use impedance matching devices
where change in the impedance occurs.

It relates to the magnitude of the voltage reflection coefficient and hence to the
magnitude of S22 for the output port and S11 for the input port.

VSWR at the input is given by the formula

VSWR at the input is given by the formula

3.9.1 Reflection coefficient:

Reflections occur as a result of discontinuities, such as an imperfection in an
otherwise

Uniform transmission line, or when a transmission line is terminated with other than
its Characteristic impedance. The reflection coefficient Γ is defined thus:

Γ is a complex number that describes both the magnitude and the phase shift of the
reflection. The simplest cases, when the imaginary part of Γ is zero, are:

 Γ = − 1: maximum negative reflection, when the line is short-circuited,

 Γ = 0: no reflection, when the line is perfectly matched,

 Γ = + 1: maximum positive reflection, when the line is open-circuited.

For the calculation of VSWR, only the magnitude of Γ, denoted by ρ, is of interest.

Therefore, we define ρ=|Γ|.

3.9.2 Return loss:

Return loss or Reflection loss is the reflection of signal power resulting from the
insertion of a device in a transmission line or optical fiber. It is usually expressed as a
ratio in dB relative to the transmitted signal power.


34

If the power transmitted by the source is PT and the power reflected is PR, then the
return loss in dB is given by

Optical Return Loss is a positive number; historically ORL has also been referred to
as a negative number. Within the industry expect to see ORL referred to variably as a
positive or negative number.

This ORL sign ambiguity can lead to confusion when referring to a circuit as having
high or low return loss; so remember:- High Return Loss = lower reflected power =
large ORL number = generally good. Low Return Loss = higher reflected power =
small ORL number = generally bad.

In metallic conductor systems, reflections of a signal traveling down a conductor can
occur at a discontinuity or impedance mismatch. The ratio of the amplitude of the
reflected wave Vrto the amplitude of the incident wave Vi is known as the reflection
coefficient Γ.

(3.40)

When the source and load impedances are known values, the reflection coefficien t is
given by where ZS is the impedance toward the source and ZL is the impedance
toward the load.

Return loss is simply the magnitude of the reflection coefficient in dB. Since power is
proportional to the square of the voltage, then return loss is given by

Thus, a large positive return loss indicates the reflected power is small relative to the
incident power, which indicates good impedance match from source to load.

When the actual transmitted (incident) power and the reflected power are known (i.e.
through measurements and/or calculations), then the return loss in dB can be
calculated as the difference between the incident power Pi (in dBm) and the reflected
power Pr (in dBm).


35


s11/s22 relationship to impedance matching:

3.9.3 Input return loss

Input return loss is a scalar measure of how close the actual input impedance of the
network is to the nominal system impedance value and, expressed in logarithmic
magnitude, is given by

By definition, return loss is a positive scalar quantity implying the 2 pairs of
magnitude (|) symbols. The linear part is equivalent to the reflected voltage magnitude
divided by the incident voltage magnitude.

3.9.4 Output return loss

The output return loss has a similar definition to the input return loss but applies to
the output port (port 2) instead of the input port. It is given by

3.10 Information on P Band

P Band: 0.2-1.0 GHz. Because lower frequencies are trapped by the ionosphere, only
frequencies above 100 MHz are available for satellite communications. The VHF and
UHF range is principally used for mobile satellite communications because the design
of the satellite and terminal hardware is relatively straightforward and well
understood. For example, the receive antenna can be a simple Yagi or wire helix. The
size and cost of terminals can also be reduced by using higher powers that are easier
to generate on board the satellite because of the low frequency being used. The
propagation of the longer wavelengths is also useful because they diffract more easily
around obstacles and are able to penetrate buildings. The main restriction in the use of
these relatively low frequencies is the competition provided by a large number of
existing terrestrial radio applications in these bands, which restricts the frequency
range available for satellite communications.


36

CHAPTER 4

SYSTEM DESIGN

4.1 Selection of the type of the design
In AWR there are two types of devices, (1) S-parameter & (2) normal device. S-
parameter device is an in-built device with S-parameters loaded from the data sheet.
There is no need of applying external bias to it, because it has fixed S -parameters (i.e.
fixed biasing).On the other hand normal device is just like any transistor device to
which any bias value can be applied. For the LNA design, S-parameter device is
chosen in general.

S-parameters do not use open and short circuit conditions to characterize a linear
electrical network; instead of matched loads are used. This termination is much easier
to use at high frequency than open and short circuit termination. Moreover the
quantities are measured in terms of power.

S-parameters are mostly used for network operating at RF and micro wave frequency
where signal power and energy considerations are more easily quantified than current
and voltages.

4.2 Selection of the transistor
Selection of the transistor is the crucial stage in LNA design. Any tr ansistor has its
NF maximum available gain (MAG) and minimum intrinsic noise figure (NF min). So
after adding the matching and biasing sections, we cannot achieve gain more than
MAG and Noise figure less than NF min. To achieve a gain over 20 dB, a 2-stage LNA
is designed. As we know, noise figure of the first stage is very crucial in the overall
noise figure, because the noise figure of the next stages is reduced by a factor equal to
the total gain till that stage.

From the comparison from many transistors like ATF 34143,ATF 54143 etc., it is
observed that Transistor ATF53189 has the Noise Figure of 0.85 dB at bias point of
4V, IDS=135 mA 2 GHz and associated Gain of 17.5dB. It has the similar parameter


37

values as the specifications of the project. Hence Transistor ATF53189 has been
chosen.

4.3 General Amplifier Design Procedures
Now that we have picked our device, stabilized it and checked it‘s maximum available
gain we can begin the process of designing the LNA. This process consists of the
following steps:-

1) Evaluate the Rollett‘s stability factor to identify the possibility of instabilities
depending on source and load matching.

2) Determine Bias conditions and circuit.

3) If a specified gain is required at a single frequency then the gain circles can be
plotted on a Smith chart and the associated source match can be read off and
the corresponding load match calculated. Careful consideration must be taken
to the position of the source match in relation to the stability circles.

4) If a specified noise figure and gain at a frequency is required then the noise
circles need to be added to the gain circles from (ii). The source match
required will be the intersection of the required gain & noise circles. Again
careful consideration must be given to the position of the source match in
relation to the stability circles.

5) Once the required source impedance has been chosen the corresponding output
match required for best return loss can be calculated.

4.3.1 Stability Design
Stability design should be the next step in LNA design.

 Unconditional stability of the circuit is the goal of the LNA designer.

 Unconditional stability means that with any load present to the output or
output of the device, the circuit will not become unstable – will not oscillate.
Instabilities are primarily caused by three phenomena: internal feedback of the
transistor, external feedback around the transistor caused by external circuit, or
excess gain at frequencies outside of the band of operation.


38

 S-parameters provided by manufacturer of the transistor will aid in stability
analysis: numerical and graphical.

 Numerical analysis consists of calculating a term called Rollett Stability Factor
(K-factor).

 When K-factor is greater than unity, the circuit will be unconditionally stable
for any combinations of source and load impedance.

 When K-factor is less than unity, the circuit is potentially unstable and
oscillation may occur with a certain combination of source and /or load
impedance present to the transistor.

The K-factor represents a quick check for stability at given biasing condition. A
sweep of the K-factor over frequency for a given biasing point should be performed to
ensure unconditional stability outside of the band of operation.

The designer‘s goal is to design an LNA circuit that is unconditionally stable for the
complete range of frequencies where the device has a substantial gain.

Different stabilization methods of LNA:

 The first one consists of resistive loading of the input. This method, although
capable of improving the stability of the circuit, also degrades the noise of the
LNA and is almost never used.

 Output resistive loading is preferred method of circuit stabilization. This
method should be carefully used because it effects are lower gain and lower
P1dB point (thus IP3 point).

 The third method uses collector to base resistor-inductor-capacitor (RLC)
feedback to lower the gain at the lower frequencies and hence improve the
stability of the circuit.

 The fourth method consists of filter matching, usually used at the output of the
transistor, to decrease the gain at a specific narrow bandwidth frequency. This
method is frequently used for eliminating gain at high frequencies, much above
the band of operation.


39

 Short circuit quarter wave lines designed for problematic frequencies, or
simple capacitors with the same resonant frequency as the frequency of
oscillation (or excessive gain) can be used to stabilize the circuit.

 The final stabilization method can be realized with a simple emitter feedback
inductor. A small inductor can make the circuit more stable at higher
frequencies. But if the source inductance is increased, the K-factor at higher
frequencies eventually falls below 1. This effect limits the amount of source
inductance that can safely be used.

 To get the best LNA stability performances have to accommodate the full
range of expected variations in operating parameters as:

 Component package parasitic
 Component values
 Temperature
 Supply voltage

 Most common causes for LNA instability are:

 Insufficient RF decoupling between supply lines of the amplifier bias.
 Parasitic inductance in GND connections.
 Excess in-band and/or out-of-band Gain.
 Electro-Magnetic coupling and Feedback.

 Always check stability of your LNA well beyond band-of-interest checking for
both, small-signal stability and for large-signal stability.

 Use stability circles on Smith Chart (for both, source and load) to verify
legitimacy of chosen Zin and Zout impedances.

In the design of transistor amplifiers it is always very important to pay attention to the
stability of the design. A common way to make potentially unstable transistors
unconditionally stable is to use resistive loading. Normally this technique is used in
the design of broadband amplifiers only because both the noise and gain performances
are significantly degraded. However, today there is a strong demand for broadband


40

circuits. There are four different ways to improve the stability with resistive loads;
series loading atthe input, series loading at the output, shunt loading at the input, and
shunt loading at the output. The load resistors that provide unconditional stability for
the transistor are normally found by studying the stability circles. It is well known
that the design equation for simultaneous conjugate match, i.e. the condition for
maximum transducer power gain, is often very useful.

4.3.2 Noise Matching and Input Return Loss (IRL)
The next step in LNA design consists of Noise Match and Input Return Loss (IRL).

 IRL defines how well the circuit is matched to 50 Ω matching of the source.

 A typical approach in LNA design is to develop an input matching circuit that
terminates the transistor with conjugate of Gamma optimum (Γopt), which
represents the terminating impedance of the transistor for the best noise match.

In many cases, this means that the input return loss of the LNA will be sacrificed.

The optimal IRL can be achieved only when the input-matching network terminates
the device with a conjugate of S11, which in many cases is different from the
conjugate of Γopt

 To design an LNA for minimum Noise Figure, determine (experimentally or
from the data sheet) the source resistance and bias point that produce the
minimum Noise Figure for that device.

 Then force the actual source impedance to ―look like‖ that optimum value
with all stability considerations still applying. If the Rollet stability factor (K)
is calculated to be less than 1 (K is defined as a figure of merit for LNA
stability), then you must be careful in choosing the source and load-reflection
coefficients.

 A typical method used in designing input matching network is to display noise
circles and gain/loss circles of the input network on the same Smith chart. This
provides a visual tool in establishing an input matching network for the best
Input Return Loss and noise trade off.


41

4.3.2.1 Using Noise Data from Datasheets
 Generally for microwave transistors following a datasheet the minimum Noise
Figure (Fmin) at higher frequencies is based on measurements, while the F mins at
lower frequencies are extrapolated.

 Fmin represents the true minimum Noise Figure of the device when the device
is presented with an impedance matching network that transforms the source
impedance, typically 50Ω, to impedance represented by the reflection
coefficient Γopt.

 The designer must develop a matching network that will present Γopt to the
device with minimal associated circuit losses. To accomplish this have to
minimize the number of components needed on the LNA input.

 The Noise Figure of the completed amplifier is equal to the Noise Figure of the
device plus the losses of the matching network preceding the device.

 The Noise Figure of the device is equal to F min only when the device is
presented with Γopt.

 If the reflection coefficient of the matching network is other than Γopt, then
the Noise Figure of the device will be greater than Fmin

 The losses of the matching networks are non-zero and they will also add to the
noise figure of the device creating a higher amplifier noise figure. The losses
of the matching networks are related to the Q of the components and associated
printed circuit board loss.

 Γopt is typically fairly low at higher frequencies and increases as frequency is
lowered.

 For FET devices larger gate width devices will typically have a lower Γopt as
compared to narrower gate width devices.

 Typically for FETs, the higher Γopt usually infers that an impedance much
higher than 50Ω is required for the device to produce F min. At VHF frequencies
and even lower L Band frequencies, the required impedance can be in the
vicinity of several thousand ohms.


42

 Matching to such high impedance requires very hi-Q components in order to
minimize circuit losses.

4.3.2.2 Different types of Input Matching
There are few topologies for matching of GaAsFETs, each of them having pros and
cons.

This low insertion loss and simple input match circuit, works well up to UHF
frequencies. There are not too many choices of tuning and a match from 50 ohms to
Gamma Optimum (best Noise Figure) depends on the FET‘s internal stray capacitance
from gate to the ground

.

 This input match gives a high performance below 500MHz.

 Can get the best Noise Figure, Gamma Optimum that can be reached.

 Because the input impedance of the GaAs FET below 500MHz is high, the Q
or Bandwidth of the input circuit can be varied with little impact on the Noise
Figure.

 The tapped L input is fine for VHF range high performance LNAs.


43

 It has very low loss, input is grounded, but the circuit has very wide
bandwidth.

 The Pi input matching network works from low frequencies up to few GHz,
and virtually can match any impedance.

 In the Pi matching network the second capacitor is tuned at a very low value,
due to the FET input stray capacitance.

 This method requires high quality capacitors.

 The stub circuit is versatile and capable of matching almost of any input
impedance, but the assembly is very large below 1GHz and relative difficult to
supply the bias voltage.

 The microstrip stub circuit is limited to microwave frequencies, is narrowband,
but has great repeatability.


44

 Just a small inductance in the gate lead can match the impedance in the 1GHz
to 2GHz region. The circuit is simple and has low loss, broad bandwidth and
excellent Noise Figure.

4.3.2.3 Output Matching
 The last step in LNA design involves output matching of the transistor.

 An additional resistor, either in series or parallel, has been placed on the
collector of the transistor for circuit stabilization.

 Conjugate matching has been exclusively used for narrow band LNA design to
maximize the gain out of the circuit.

 With additional IP3 requirement forced on the LNA, the trade-off between IP3
and gain must be considered.

 Linearity matching is widely known by high-power amplifier designers. The
so-called load pulling is used to establish IP3 and gain impedance contours.
The load pulling can be realized by using the non-linear Spice model ofthe
transistor with simulation software.

 Harmonic balance can be used for establishing two-tone environment.

 In order to improve the gain and noise response of the final stage in the
cascade design, we need to provide the RL = ROUT*.

4.3.3 Real issues in LNA design
 An LNA is a design that minimizes the Noise Figure of the system by
matching the device to its noise matching impedance, or Gamma optimum
(Γopt).

 Gamma optimum (Γopt) occurs at impedance where the noise of the device is
terminated.

 All devices exhibit noise energy. To minimize this noise as seen from the
output port, one must match the input load to the conjugate noise impedance of
the device.


45

 Otherwise the noise will be reflected back from the load to the device and
amplified. While this gives a minimum noise figure, it often results in slightly
reduced gain as well as possibility increasing the potential instabilities.

 Noise match often comes close to S11 conjugate (S11*) under non-feedback
conditions.

 As a result, the input impedance to the amplifier will not be matched to 50
ohms. Γopt, as presented in data sheets, is the actual measured load at which
the minimum noise figure is found.

 Designing an effective low noise amplifier (LNA) requires a high-performance
transistor. But most suitable devices are potentially unstable at microwave
frequencies, leading to oscillation. Fortunately, resistive loading at the input or
output of the transistor can prevent oscillation at the frequency of interes t for
all passive source and load termination but stability at other frequencies
remains problematic, and out-of-band oscillations are possible.

A further complication on LNA design is that the input load of the amplifier is usually
less than ideal. It is either connected to an antenna, which can change its impedance
with changing the environment, or to a filter, which by very physics of a reflective
network will have very bad match out of band. These mismatches could cause the
device to become unstable out of band and some cases in band. As the gain of the
device increases, the difficulties in yielding a stable design become increasingly more
challenging.

To avoid overloading the LNA, an input filter is commonly used. Since the device is
not matched to S11*, the input of the LNA will not be 50 ohms. This can cause
distortions in the pass band of the filter when connected to the input of the LNA, as
filter are intended to operated in their characteristic impedance, typically 50 ohms.

Printed inductors or transmission lines are free as compared to SMT inductors, which
typically cost 10 to 25 times as much as resistors or capacitors in volume. Printing an
inductor is easy and results in highly repeatable results. Printed inductors usually
exhibit poor Q due to the lossy dielectric, and, if a ground plane exists, they are no
more than a high impedance transmission line.


46

As shown a transmission line can replace an inductor to some degree, but inductors
and high impedance transmission lines have a different trajectory on the Smith Chart.
High impedance transmission line can be made to look more like printed inductors in
cases where the backside of the PCB is suspended away from a grounded chassis. This
is accomplished by removing the backside ground plane of the PCB directly under the
printed inductor.

In this case beware of digital noise coupling into the input of the LNA from circuitry
on the opposite side.

 The next concern is what load impedance to match. Remember matching to the
conjugate of S22* is only valid if the input is conjugate matched. Since S12 is
non-zero, whatever load is present to the input will cause the output load
change.

 Another issue is stability, especially if a filter is going to be used at the input.
The output port can potentially give difficulties since the input is very
restricted by its match.

Real components differ from ideal ones in several respects. First, real components
have a price associated with them. There is a trade-off between price and performance
of these parts. The competitiveness of today's markets often forces designers to use
inexpensive components in their designs.

 Real discrete components have a finite resistance called Equivalent Series
Resistance (ESR). The ESR introduces losses that result in lower gain and
noise figure. Although typically only a few tenths of an ohm in value, ESR will
affect the matching networks.

 Discrete components also have a Q value, measured at a particular frequency
that can contribute to unwanted resonance.

 High-Q networks are sensitive to variations in process, voltage, temperature,
and component value.

 A component's Series Resonant Frequency (SRF) is the frequency where it
will behave erratically.


47

 If an inductor is operated at or above its SRF, it might behave as a capacitor.
To avoid this, select components where the SRF is much higher than the
operating frequency.

 Also, leaded through –hole parts have leads that add series inductance to a
design, and surface-mount parts have pads that add shunt capacitance to a
circuit.

4.4 Gain & Noise Parameters
Using the S-parameters of the device it is possible to calculate the overall transducer
gain which consists of three parts, the gain factor of the input (source) matching
network, the active device and the output (load) matching network: -

(4.1) (4.4)

(4.2) (4.5)

(4.3) (4.6)

Overall Transducer gain =10LOG10 (Gs .Go .GL )

4.5 Constant Noise circles
Formula for calculation of noise circles:-

| |

Where

F= required noise figure

Fmin= Optimum noise figure

RN =Equivalent noise resistance of transistor

Γopt = Reflection coefficient to achieve optimum noise

Centre of noise figure circle = ΓoptN+1

And the radius of the noise figure circle is


48


√ ( | |)

4.6 LAYOUT RULES
There are certain rules which were followed in the layout design

 No two devices must be connected back to back.

 Use MLIN between components.

 Use MTEE$ / MCROSS$ whenever there is a junction, Extend the junction
arms using MLIN.

 Grounding must be done using via.

 Break schematic in to Sub circuits.


49

CHAPTER 5

DESIGN & IMPLEMENATION

5.1 DESIGN FLOW
This design flow will explore the design parameters space of integrated inductively-
low noise amplifiers (LNA), under the constraint of matched input impedance, is
presented. It is based on AWR microwave simulation tool and can be easily
automated. The method is applied to the design of a (0.05-1) GHz LNA with less than
4dB noise figure (NF) for a fixed bias current.


50

5.1.1 Transistor selection
PHEMT (Pseudomorphic High Electron Mobility Transistor) transistors find wide
market acceptance because of their excellent low noise figures and performance. The
transistor is also selected depending up on the frequency range, noise figure and gain
that are given in the specification.

The data sheet provides the device‘s small signal S parameters, which must be rea d
into the simulator in order to calculate the transistor parameters. The S Parameters of
the transistor with different bias points are available with the transistor datasheet. The
transistor with the bias point of -4v, 60mA is selected, which can give better
performance at this bias point.

5.1.2 Stability check
When embarking on any amplifier design it is very important to check on the stability
of the device chosen, otherwise the amplifier may well turn into an oscillator. The
main way of determining the stability of a device is to calculate the Rollett‘s stability
factor (K), which is calculated using a set of S-parameters for the device at the
frequency (0.5 to 18GHz) of operation. For the device to be unconditionally stable,
the stability circles should lie outside the circle for |S 11 |<1 and |S 22 |<1.

5.1.3 STABILITY ENHANCEMENT
Resistive loading
 A transistor can be stabilized by adding small series resistors or large shunt
resistors to its input or/and output.

 These lossy elements ensure that the transistor cannot be presented with
impedances inside the instability regions, irrespective of what source and load
impedance are connected.

Series Resistance Stabilization Method
Steps:

1. Convert Transistor S-parameters to Z-Parameters

2. Add series resistance to real part of Transistor Z22

51

3. Convert composite Z-Parameters to S-Parameters

4. Check K

5.1.4 INPUT MATCHING CIRCUIT
The matching for lowest possible noise figure over a band of frequ encies requires that
particular source impedance be presented to the input of the transistor. The noise
optimizing source impedance is called as Gopt, and is obtained from the
manufacturer‘s data sheet.

Figure 5.1(a) input matching circuit

The above circuit shows the input matching circuit. The input matching circuit is
matched to noise optimizing source impedance 0.78∟30 called as Gopt, and is
obtained from the manufacturer‘s data sheet.

Figure 5.1(b) layout of input matching circuit


52

The 1st stage has no matching on the output and as we require a good output return
loss we should match to S22*. Note S22 will now have been modified by adding the
input matching circuit and will have to design the matching circuit to be the conjugate
of S22modified (This is because S22 is looking into the device and the conjugate will
looking towards the matching circuit.

The process of layout involves the interconnection of MLINS, Tees between the
elements. The layout obtained for the input matching network shown in schem atic
5.8(a) is shown in above figure 5.8(b).The layout has certain constraints that the width
and the length of MLIN, MTEE, should be not less than 0.025mm.

5.1.5 OUTPUT MATCHING CIRCUIT

Figure 5.2(a) Schematic of output matching circuit

The above figure 5.12(a) shows the schematic of output matching network followed
by interconnecting the MLINS and MTEE for layout purpose. In order to improve the
gain and noise response of the second stage we need to provide the RL (7.6891 -
7.0605i).

In order to improve the gain and noise response of the final stage we need to provide
the RL = ROUT* given by:

( )


53

The value of S1 of the output matching is calculated and layout is shown below

This composite design using ideal elements was then optimized. Finally, the ideal
elements were replaced with vender elements and the design was again optimized.
After this step, the layout process was started.

The layout process involved interconnecting appropriate bends, tees, and MLINs to
the optimized LNA design with vender elements.

Figure 5.2(b) layout of output matching circuit

The layout of output matching network is shown in the above figure 5.2(b). The long
length MLIN and inductor shown in the fig 5.2(b) is used to take RF output.

5.2 IMPLEMENTATION OF THE DESIGN
The design implementation requires adding microstrip lines between the lumped
elements and placing of micro strip Tee at the junction. The junction arm has to be
extended using MLINS. The grounding must be done using via.

The design is implemented on FR4 substrate with the relative permittivity =4.4 with
a height of 1.6mm. The substrate thickness is chosen to be 0.035mm, Rho=1.

The below figure shows the sub circuit of final schematic of an amplifier, the first sub
circuit represents the input matching network. The second block shows the first stage
of stabilized transistor. The inter-stage matching network is represented in third
block. The fourth block represents second stage and the output matching network is
represented in the last block.


54


Figure 5.3 Sub circuit of the schematic.

This circuit component models a length of Micro strip Transmission Line. The model
assumes a Quasi-TEM mode of propagation and incorporates the effects of dielectric
and conductive losses. The parameters W (Strip Width) and L (Strip Length) are
lengths entered in the default length units. Some of the restrictions need to be
followed while implementing in AWR-MWO simulator is listed below:

0.05 ≤ W/H ≤ 20 Recommended
T/W ≤ 0.5 Recommended
T/H ≤ 0.5 Recommended
εr ≤ 16 Recommended
1 ≤ εr required
Tand ≥ 0 Required
0 ≤ Rho ≤ 1000 Required
0 ≤ Rho ≤ 100 Recommended

The selected device will not be stable, so the device is made unconditionally stable by
adding resistive loading which is one of the methods to make the device stable for the
entire range of frequency. The supply voltage to the drain and the gate o f the
transistor are provided through MLEF whose arm is extended through MLIN.

The transistor and resistors makes use of MLIN and tee for connection purpose. The
recommended ratio of width and length should not be less than 0.05mm.

The grounding is done through vias which has the diameter of 0.254mm. The ratio of
width and length should not be less than 0.254..


55

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