3. 2.1 – Sample & Hold (S&H) Circuit - continued
Control Signal
Rate of change of the output voltage when the control signal is in
the hold state ‐ due to leakage current.
4. 2.1 – Sample & Hold (S&H) Circuit - continued
Ideally =0 & it should be too small.
needed for the capacitance to achieve 0.993 Vi ≈ 0.7 % error.
5. 2.2 – Analogue-to-Digital (ADC)
DC level
n bits O/P
I/P Quantizer Encoder
Full Scale
ADC
After Sampling; the amplitude of the analogue samples is quantized & encoded using
either uniform or non-uniform quantization & encoding depending on the application
6. 2.3 – Quantization
• The quantizing operation approximates each sample value to the
nearest level in a finite set of discrete levels/values, known as
quantization levels.
• This approximation introduces quantization error. Therefore, once
quantized, the instantaneous values of the signals are lost, and can
never be reconstructed exactly.
Continuous signal values Discrete signal values
at discrete times at discrete times
Quantizer
7. 2.3 – Quantization (cont.)
• Quantization principle is based on that any human sense
(ear & eye) can only detect finite intensity differences.
as an ultimate receiver
There are 2 types of quantization:
1. Uniform quantization: biomedicine, audio systems.
2. Nonuniform quantization: communication systems for the need to compress
signals.
8. 2.3.1 – Uniform Quantization & Encoding
• The full scale range of the I/P signal is divided into 2n values; (n is the number of ADC bits).
• Each analogue sample is assigned to one of the 2n values by truncation.
• The difference between two adjacent values is called ‘Quantum’ or step size (a)
Vmax
111 3.5 a
110
e 2.5 a
n = 8 levels
Signal level
1.5 a
0.5 a 0
-0.5 a
010 -1.5 a VFSR
001
a -2.5 a
000
-3.5 a -Vmax
Unipolar (+Vm or ‐ Vm)
polar (±Vm)
FSR: Vmax - Vmin (swing). Mid‐tread Quantizer.
L: number of quantization levels L= 2n – 1
L= 2n Mid‐rise Quantizer.
n increases for audio applications as the ear is more sensitive than the eye.
9. 2.3.1 – Uniform Quantization & Encoding - Continued
Quantization Transfer Characteristics
Mid‐
tread
a=Q
Truncation leads to quantization noise
• Quantization noise is random & follows a zero-
mean uniform distribution (pdf). a/2
0
- a/2
Quantization Noise
11. 2.3.1 – Uniform Quantization & Encoding - Continued
rms
Not detected by ADC
12. 2.4 – Digital-to-Analogue Converter (DAC)
• What is a digital to analog converter (DAC)?
– Converts digital input signal to an analog output
signal
Bn-1 B0
1 0 0 0 1 1 1 Va
0 1 0 1 0 0 0
0 0 1 1 0 1 1 DAC
1 1 1 1 1 0 1 Circuit Symbol
B0
LSB
B1
B2
n: word‐length
MSB
13. 2.4 – Digital-to-Analogue Converter (DAC)…Cont.
• D/A conversion can be achieved
using a number of different
methods such as:
– The Weighted-Resistor DAC
– The Ladder Network (The R-2R Ladder DAC)
– The Switched Current-Source DAC
– The Switched-Capacitor DACs
14. 2.4.1 – Weighted Resistor DAC
Rf = R
∑I i
R 2R 4R 8R Vo
Most • summing amplifier
Significant
Bit
Least
Significant Bit
VREF
Large n very large R
16. 2.4.1 – Weighted Resistor DAC - continued
Advantage
– Easy principle (low bit DACs)
Disadvantages
– Requirement of several
different precise input
resistor values: one unique
value per binary input bit.
(High bit DACs)
– Larger resistors ~ more error.
– Precise large resistors –
expensive. VREF
17. 2.4.2 – R-2R Ladder Type DAC
R-2R Ladder Network
18. 2.4.2 – R-2R Ladder Type DAC (Cont.)
D 0 × 2 0 + D1 × 21 + D 2 × 2 2 + D 3 × 2 3
Vo = 4
Vref
2
Example: Circuit with 0110 input
19. 2.4.2 – R-2R Ladder Type DAC - continued
VREF
MSB
LSB
20. 2.4.2 – R-2R Ladder Type DAC - continued
• The less significant the bit, the more resistors the signal must
pass through before reaching the op‐amp
• The current is divided by a factor of 2 at each node
LSB MSB
21. 2.4.2 – R-2R Ladder Type DAC - continued
Rf ⎛ B2 B1 B0 ⎞
VOUT = VREF⎜ + + ⎟
R ⎝2 4 8⎠
Rf
22. 2.4.2 – R-2R Ladder Type DAC - continued
• Question:
– Input = (101)2
– VREF = 10 V
– R = 2 kΩ
– Rf = 2R
R R R 2R
R 2R 2R 2R
I0 I0
Op-Amp input
VREF VREF
“Ground”
B0 B2
23. 2.4.2 – R-2R Ladder Type DAC - continued
• Only two resistor values‐ R and 2R
• Does not need the kind of precision as Binary
weighted DACs
• Easy to manufacture
• More popular
• Less errors
24. 2.5– DAC Resolution
• Resolution: is the amount of variance in
output voltage for every change of the LSB in
the digital input.
• How closely can we approximate the desired
output signal(Higher Res. = finer detail=smaller
Voltage divisions)
• A common DAC has a 8 ‐ 12 bit Resolution
VRef
Resolution = VLSB =
2n
25. 2.5– DAC Resolution (Cont.)
• Voltage
Vref
resolution:
2n
Voltage step example : for 10 bit resolution. So n=10
if Vref = 10V
voltage step : 10V/1024 = 10mV
26. 2.5– DAC Resolution (Cont.)
Poor Resolution(1 bit) Better Resolution(3 bit)
Vout Vout
Desired Analog Desired Analog signal
signal
111
110 110
2 Volt. Levels
1
8 Volt. Levels
101 101
100 100
011 011
010 010
001 001
0 0 000
000
Digital Input Approximate Digital Input
Approximate
output output
