1. 2nd
Order Active Filter Prototype 1 of 10
Generalised 2nd Order
Active Filter Prototype
Adrian Mostert
Bachelor of Electronic Engineering – Year 3
Dept of Electronic Engineering
Cork Institute of Technology,
Cork
1 Overview
The widely used Sallen-Key
configuration, also known as a voltage-
controlled voltage source (VCVS), was
first introduced in 1955 by R.P. Sallen
and E.L. Key of MIT’s Lincoln Labs.
The Sallen-Key filter is a popular 2nd
order filter circuit that students learn in
colleges and universities as part of
analogue electronics design theory.
The problem with college is that often a
lot of lab time is spent breadboarding
circuits which is often aggravated by
faulty components or lab equipment
when the time could be better spent
analyzing a prebuilt circuit.
By having a pre-built generalised Sallen-
Key filter circuit lab time can be
maximised for measuring and recording
the input/output signals of the circuit and
thus alleviate the frustration and pressure
associated with lab time by students.
The goal of this project is to produce an
educational tool with accompanying
documentation and simulation files for
use by undergraduate students and
lecturers which will demonstrate the
Sallen-Key 2nd Order Active filter in 4
modes: bandpass, bandstop, lowpass and
highpass.
Having a preassembled circuit prototype
requiring only minor changes for it to be
reconfigured will cut the time spent by
students building the circuit in the lab
and if maintained it will help eliminate
problems with faulty components.
Sallen-Key filters are an important part
of analogue electronic theory and can be
challenging mathematically as the
calculations for the transfer function
equations can be lengthy and tedious and
are frequently not understood properly;
as mentioned previously building the
different circuit variations in the lab is
time consuming and mistakes are often
made and faulty components result in an
unsatisfactory teaching/learning
experience.

2. 2nd
Order Active Filter Prototype 2 of 10
The stakeholders have been identified
primarily as being college graduates but
the lecturers will also benefit from the
time saved using the product.
The cost of producing the board has
been minimal as the components were
readily available from the department
store and the etching of the board was
done in the college lab and did not have
to be outsourced.
There was some supervision by the Lab
Technician, Gary O’Dwyer during this
process but it did not take more than 2
hours to successfully etch and populate
the board.
Organizations involved are primarily the
Cork Institute of Technology, support
provided by the supervisor in the form of
weekly meetings and some assistance
from college staff during the etching
process was required but no outside
consultants were employed.
.
2 Objectives
The primary objectives are to save the
lecturer and student time by delivering a
simple preassembled circuit board the
configuration of which can be changed
quickly by following the instructions
with appropriate preselected components
thus eliminating the possibility of bread
boarding errors and faulty lab
components in order to investigate the
particular action of a 2nd
order active
filter circuit.
Secondary objectives are to deliver
teaching materials in the form of
thorough mathematical explanation of
the equations and transfer functions
required for circuit analysis.
A CD containing proteus and MATLAB
files will be provided for this purpose to
allow the student to simulate the circuits
quickly and solve quadratic equations
for determining the cutoff points without
prior knowledge of the MATLAB
language.
Further objectives include the
improvement of my own engineering
mathematics ability and analogue circuit
analysis as a consequence of creating the
comprehensive learning material.
It is hoped that the project can be
extended to fourth year where it can be
developed further for the study of digital
signal processing.
3 Market Research
An informal survey was conducted with
three 4th
year electronics undergraduates
at CIT who were interviewed to get their
opinions on the idea of a generalized
circuit prototype board to discuss the
potential benefits.
The opinion was that a device of this
type would indeed prove beneficial to
the undergraduate and graduate student
alike, save lab time and the
documentation would assist with
assimilation of the circuit theory.
Such a product is not available
commercially to and no competitors
have been identified

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Order Active Filter Prototype 3 of 10
4 System Design
The following block diagram is a
representation of the design process and
work flow followed for this project.

4. 2nd
Order Active Filter Prototype 4 of 10
5 Schedule
The proposed schedule plan for the
project shifted considerably during the
time span mainly due to adjustments that
had to be made as a result of problems
encountered at various stages.
Task 1: Design solution for existing
problem using core project idea began 1st
Feb and came to an end around the 18th
as expected.
Task 2 : Meet with stakeholders
remained active until the 16th
March by
which time all the stakeholders had been
interviewed the schedule for this task
had to be adjusted on more than one
occasion after cancellations by the
stakeholders.
Task 3: Simulation of Individual circuits
was the most difficult to predict as it was
an ongoing process and lasted until the
last quarter of the scheduled time but
had to be adjusted numerous times due
to obstacle encountered in the design
process for which meetings with the
supervisor had to be scheduled.
Task 4: Research ideal vs practical op
amps was a short time dedicated
exclusively to this important issue. It has
one dependent.
Task 5: Derive Equations for Individual
Circuits dependent on task 4 as work on
derivation could not commence before
finalizing the design.
Task 6: The coding in MATLAB
commenced towards the end of Task 5
but was not entirely dependent on its
completion so it was not set as a
dependent.
Task 7: Additions to the Mini-report
were ongoing and the timeline was
amended to reflect this.
Task 8: Completed as scheduled no
amendment made.
Task 9: Finalisation of the schematic
was the first milestone.
Task 10: Ordering and arrival of
components completed on time. One
depended – Task 11.
Task 11: Work of etching the pcb could
begin before all parts had arrived.
Task 12: Populating the pcb was
dependent on completion of the etching
process.
Task 13: Proper testing was not possible
before completion of the preceding task.
Task 14: Documented learning material
milestone reached.

5. 2nd
Order Active Filter Prototype 5 of 10
Task 15: Packaging of proteus files
completed.
Task 16: Deliver of final presentation
milestone was amended to 12th
May.
6 Testing – Results
The first draft of the schematic provided
revealed problems with the simulated
analogue output. As a working circuit
was to be eventually constructed
research regarding existing Sallen-Key
topologies for the purposes of
comparison with the existing design
began. Another aspect of the design that
much time was spent researching was
the variations in signal response using
different op-amp models apart from the
741 such as uA741, LM741 TH3001 and
LM101A it was thought that an
internally compensated amp would
improve the performance of the circuit.
Rigorous trial and error was carried out
at this time as the following graphics
show.
Figure 1. An attempt to calm the saturating
integrator with a resistor R1 in parallel with
feedback capacitor.
Although the output can not be seen in
this screenshot, it is still saturating.
The following table is a log of steps
carried out in an attempt to prevent the
op amp from going into saturation.
As can be seen, the original schematic had
a negative feedback loop to provide some
gain but it was eventually agreed to discard
this as there was already positive feedback
and the resultant combination of both types
of feedback was becoming too confusing
and the inverting input was eventually tied
to ground.
Figure 2 Investigating the use of an variable
series resistor in line with C3 to counteract
voltage offset.

6. 2nd
Order Active Filter Prototype 6 of 10
It was thought that by adjusting for the
offset voltage it would prevent the amp
from going into saturation however this
proved unsuccessful.
7 Achievements
Several research documents including
application reports and books listed in
the Bibliography were used to research
Sallen-Key architecture for a historical
perspective and compared standard
Sallen-Key circuits with the specific
generalised topology.
The generalised topology was found to
differ in one particular aspect from
standard ideas in so far as a signal to
ground path on the non-inverting input.
Request was made to alter the specific
generalized topology to more standard
form but was not permitted.
During the ensuing experiments it was
found not possible to simulate a
satisfactory output for more than one
type circuit i.e. BP and LP without
altering the specific topology in the
simulation.
Assurance was given that the
mathematical derivations would prove
out and this they did. However, it was
found that the generalized topology as it
is presented is not implementable in
practice.
Further research was done on ideal vs
practical op-amp models, the integrator
in particular and an attempt was made to
calm the saturating output by
introducing a resistor in parallel with the
capacitor in the positive feedback path.
Very marginal success was achieved
with this and it was eventually discarded
not appropriate to the solution. Attempts
at altering the amplitude of the input test
signal from very small to between 5 or
10 volts yielded no effect on the
saturation.
A load resistor was introduced to
provide a resistance at the output, after
several experiments this also was
abandoned and attention to the practical
was turned instead to the derivation of
equations describing the frequency and
phase angle response.

7. 2nd
Order Active Filter Prototype 7 of 10
7.1 Block C.
Work began with derivation of the
generalised transfer function; of
particular use as a reference were some
class notes on Sallen-Key filters and
filter transfer functions from the
previous semesters Electronic
Engineering module. Additional reading
was necessary to fully appreciate the
finer concepts and several sources were
consulted for this purpose which are
listed in the bibliography.
The kind assistance of the lecturer as
well as one particularly gifted class mate
was enlisted on more than one occasion
during the process which allowed the
generalized equation to be realized.
7.2 Block D3.
Once the gain of the -3db points had
been worked out using properties of the
key equations derived in Block C the
specific equation was rearranged into a
quadratic form the roots of which would
provide the cutoff points fc1 and fc2.
Because of the unwieldy size of the
equation it was preferable to resolve it
using a maths package. MATLAB was
selected for the task and a simple script
constructed as follows:
Output values for the bp circuit were:
𝑓𝑐1 = 5.1644 kHz
𝑓𝑐2 = 247 Hz
7.2 PCB Layout
The pcb layout was executed in Proteus
Ares. The footprint of the minres100k
element was decomposed and the
distance between the through holes
extended to allow more room when
inserting/removing leads of the
components.
Single inline pin sockets as above were
soldered into the lead holes of the Z
block components to allow their
insertion/removal without soldering.

8. 2nd
Order Active Filter Prototype 8 of 10
Figure 3 Prototype model
Figure 4. PCB layout
The circuit ws constructed and tested in
the lab.
7.3 7.3 Blocks E,F,G
The bandpass circuit was simulated and
the frequency and phase angle response
plotted as follows.
Figure 5. Frequency and Phase Angle
Response Plot
As can be seen the values taken from the
simulated frequency plot and phase
angle are within less than 1% of error the
values acquired by using the
mathematical equations. The linearity of
the phase angle plot can also be seen
here.
Figure 6. Bandpass circuit
The prototype was configured in the lab
using the same component values as in
this schematic and the resultant output
matched faithfully with the simulated
response with the amp saturating to the
negative rail.
8 Project Progress
Assessment
The schedule that was set for tasks in
the Gantt chart had been thought out
well and was adhered to relatively
easily.
The usefulness of the Gantt chart in a
more organized environment can be
appreciated and even better attention to
using the software will be given in the
future where the schedule will be kept
more simple and linear with fewer
dependencies. If used collaboratively it
is easy to see how useful a tool it can be.

9. 2nd
Order Active Filter Prototype 9 of 10
9 Next Tasks
The next section of work entails proving
out the generalized equation for the
remaining 3 circuit types against the
simulated models. Also there are
possible errors in the phase response for
the bandpass type which might have to
be reworked. This has to be done before
the remaining learning material can be
set out.
The main problem I foresee is that I will
not be permitted to rework the circuit to
a more standard form so as to be able to
produce a working prototype.
It was discovered that the signal
input/output block on the pcb had been
erroneously labelled which will be fixed
in future versions.
10 Conclusion
It was understood from the start that the
project would entail circuit analysis,
derivation of transfer functions and
presumably construction of a working
circuit. The material had been covered in
a previous semester which included labs
but it was felt that not enough
confidence had been acquired during this
time and it was hoped that that would
improve by performing the maths and
doing the analysis for the learning
material which was why the project was
chosen.
Instinct upon receiving the brief was to
simulate it straight away which was done
– the frequency and phase angle
response were computed by the
simulation software and meaningful
graph data was be plotted but upon
investigating the simulated signal output
of the circuit it was disheartening to find
the signal distorted.
This lead to investigation of the Sallen-
Key type circuit and no shortage of
examples were found however it was
realized that the particular topology that
had been given seemed non-standard
compared to other sources. This was no
deterrence at first but after further
investigation and trial and error it was
understood that the circuit was probably
not going to work as expected. The gap
between the ideal and the practical
seemed to be widening.
As assurance had been given that the
mathematical representation would work
out this was pursued in favor of the
practical application and the circuit
abandoned to better focus on the
mathematics of the frequency and angle
response.
The source of reference was primarily
class notes as they seemed simple
enough to follow however frequently
obstacles to understanding were
encountered which required outside
assistance despite having access to
numerous text books.
As a consequence of this project there
has been a marked improvement in the
confidence and ability to do transfer
function derivations and analog circuit
analysis; also awareness of the subtleties
involved in design and prototyping
thereof. The exercise of writing this
report has also proved beneficial in
terms of the academic process and
awareness.
REFERENCES
[1] Hank Zumbahlen, “Phase Relations
in Active Filters”, Analogue Dialog
Volume 41, Number 4, 2007
www.analog.com/library/analogDial
ogue/cd/vol41n4

10. 2nd
Order Active Filter Prototype 10 of 10
[2] Walt Jung, “Op Amp Applications
Handbook”, (Newnes, 2006),
http://www.analog.com/library/analo
gDialogue/archives/39-
05/op_amp_applications_handbook.
html
[3] Analysis of the Sallen-Key
Architecture, Application Report,
SLOA024B, Texas Instruments, July
1999,
http://www.ti.com.cn/general/cn/doc
s/lit/getliterature.tsp?baseLiteratureN
umber=sloa024&fileType=pdf
[4] Bruce Carter and Ron Mancini, OP
Amps For Everyone, third edition,
Oxford: Elsevier, 2009
[5] Clayton R. Paul, Analysis of Linear
Circuits,Mc Graw Hill University of
Kentucky,1989
[6] Theodore F Bogart, Jr, Linear
Electronics, McMillan, University of
Southern Mississippi, 1994