Analog to Digital , Digital to Analog Conversion

1. ANALOG TO DIGITAL &
DIGITAL TO ANALOG CONVERSION
Prepared by:-
Kunj Patel (140410116058)

2. ANALOG-TO-DIGITAL CONVERTERS
 Why Analog?
• Not everything is digital!
• Even digital signaling has analog aspects (!?)
• Analog circuits and analysis are still necessary
• Physical phenomena (i.e., the real world) are
usually analog
• Many sensors are analog (potentiometer,
phototransistor, thermo-sensor, microphone)
• Many actuators are analog (solenoid, speakers)
• Some signals need to be processed in analog domain
before conversion to digital (amplification, filtering,
linearization)

3. ANALOG-TO-DIGITAL CONVERTERS
proportionality
Vmax = 7.5V
0V
1111
1110
0000
0010
0100
0110
1000
1010
1100
0001
0011
0101
0111
1001
1011
1101
0.5V
1.0V
1.5V
2.0V
2.5V
3.0V
3.5V
4.0V
4.5V
5.0V
5.5V
6.0V
6.5V
7.0V
analog to digital
4
3
2
1
t1 t2 t3 t4
0100 1000 0110 0101
time
analoginput(V)
Digital output
digital to analog
4
3
2
1
0100 1000 0110 0101
t1 t2 t3 t4
time
analogoutput(V)
Digital input

4. ANALOG TO DIGITAL CONVERSION
Instantaneous amplitudes of
continuous analog signal, measured
at equally spaced points in time.
A series of “snapshots”
Error=1/2 LSB

5. ANALOG TO DIGITAL CONVERSION
5
[a.k.a. “sample word length,” “bit depth”]
Precision of numbers used for
measurement: the more bits, the higher
the resolution.
Example: 16 bit
Sampling Rate
How often analog signal is measured
Sampling Resolution
[samples per second, Hz]
Example: 44,100 Hz

6. SAMPLING RATE
6
Nyquist Theorem:
Sampling rate must be at least twice as high as
the highest frequency you want to represent.
Determines the highest frequency that you
can represent with a digital signal.
Capturing just the crest and trough of a sine
wave will represent the wave exactly.

7. DIGITAL AND ANALOG CONVERSION
 A/D transfer function:
 10-bit ADC converter
 1024 voltage levels between 0V and
VREF
 10-bit digital value
 Usually VDD=VREF
 (e-Vmin)/(Vmax-Vmin)=d/(2^n-
1),
 When Vmin=0:
 e/Vmax=D/(2^n-1)
 In general
 Vmax match 2^n-1
 Vmin match 0
 How does D/A and A/D
conversion work?

8. DIGITAL AND ANALOG CONVERSION
 D/A is simpler than A/D
 Different resisters and an inverted OpAmp, to
implement a weighted summer.
 Example: 4-bit D/A
 If D3D2D1D0=0001 (i.e., 0V,0V,0V,-5V)
 Vo=-1.1*(D0/17.6+D1/8.8+D2/4.4+D2/2.2)
=0.3125V
 If D3D2D1D0=1111 (i.e., -5V,-5V,-5V,-5V)
 Vo=-1.1*(D0/17.6+D1/8.8+D2/4.4+D2/2.2)
=4.6875V

9. DIGITAL AND ANALOG CONVERSION
 Use D/A converter to generate
different analog values and
compare
 Control logic decides which values to try
 When comparison complete, best match
is put on output
 How can D/A be matched to
input in fewest steps?
comp
VIN
D/A
converter
A/D control
logic
10-bit test value
clock
10-bit output
start
conversion
conversion
complete

10. SUCCESSIVE APPROXIMATION (SAR) ADC
 Matching strategies:
 Counting conversion (slow)
 Successive approximation (faster)
 Successive Approximation:
 Basically binary search:
 Exact 10 steps instead of
1024, SAR is fast!
XXX
0XX 1XX
00X 01X 11X10X
000 001 010 011 100 101 110 111
XXX
<100?
0XX
<010?
1XX
<110?
00X
<001?
01X
<011?
10X
<101?
11X
<111?

11. DIGITAL-TO-ANALOG CONVERSION USING
SUCCESSIVE APPROXIMATION
Given an analog input signal whose voltage should range from 0 to 15 volts, and an 8-bit digital encoding, calculate the correct encoding for
5 volts. Then trace the successive-approximation approach to find the correct encoding.
5/15 = d/(28 - 1)=d/255
d= 85
Successive-approximation method
0 1 0 0 0 0 0 0
Encoding: 01010101
½(Vmax + Vmin) = 7.5 volts
Vmax = 7.5 volts.
½(7.5 + 0) = 3.75 volts
Vmin = 3.75 volts.
0 0 0 0 0 0 0 0
0 1 0 0 0 0 0 0½(7.5 + 3.75) = 5.63 volts
Vmax = 5.63 volts
½(5.63 + 3.75) = 4.69 volts
Vmin = 4.69 volts.
0 1 0 1 0 0 0 0
½(5.63 + 4.69) = 5.16 volts
Vmax = 5.16 volts.
0 1 0 1 0 0 0 0
½(5.16 + 4.69) = 4.93 volts
Vmin = 4.93 volts.
0 1 0 1 0 1 0 0
½(5.16 + 4.93) = 5.05 volts
Vmax = 5.05 volts.
0 1 0 1 0 1 0 0
½(5.05 + 4.93) = 4.99 volts 0 1 0 1 0 1 0 1

12. 3-BIT QUANTIZATION
A 3-bit binary (base 2) number has 23 = 8 values.
0
1
2
3
4
5
6
7
A rough approximation
Amplitude
Time — measure amp. at each tick of sample clock

13. COMMON SAMPLING RATES
Sampling Rate Uses
44.1 kHz (44100) CD, DAT
48 kHz (48000) DAT, DV, DVD-Video
96 kHz (96000) DVD-Audio
22.05 kHz (22050) Old samplers
Most software can handle all these rates.
Which rates can represent the range of
frequencies audible by (fresh) ears?