Delta modulation is a simplified form of differential PCM where a 1-bit word indicates if the current sample is greater than or less than the previous sample. This results in a staircase approximation of the input signal. The step size Δ is important, as too large causes granular noise when the input changes slowly, and too small causes slope overload distortion when the input changes rapidly. In this lab, the student investigated these effects of delta modulation using PSpice simulations. Both sine and square wave inputs were tested, and the results showed the tradeoff between large and small Δ values. The student learned that the best choice for Δ is a medium value that avoids both types of distortion.

1. Delta Modulation
Formal Element
Junaid Malik, DT008/2
Group A
Submission Date: 14/12/12

2. JunaidMalik,
DT008/2, GroupA
Objective:
The objective of this laboratory was to investigate delta modulation and to examine slope
overload distortion and grenulon noise.
Introduction:
Delta modulation is a simplified form of differential Pulse Code Modulation (DPCM) where a
1-bit word is used to indicate whether the current sample value is less than or greater than
the previous sample value. In effect we approximate the input analogue signal with a stair
case function with a step size.
The step size is very important in designing a delta modulation system. Large values of Δ
cause the modulator to encounter rapid changes in the input signal but at the same time
because a large quantization noise when the input changes slowly. For large Δ, when the
inputs varies slowly, a large quantization noise occurs, which is known as granular noise.
When there is a case of a too small Δ, we have problems as rapid changes occur in the input.
When the input changes rapidly it takes a long time for the output signal (staircase) to
follow the input and an excessive quantization noise is caused in this period. This type of
distortion is caused by high slope of the input waveform; it is called slope-overload
distortion.
In delta modulation the quantizer is a 1-bit (two-level) quantizer with plus or minus delta.
The one-bit quantizer is a comparator which reports on whether the predicted sample value
is less than or greater than the actual sample value.
𝑇ℎ𝑒 𝑝𝑟𝑒𝑑𝑖𝑐𝑡𝑜𝑟 𝑒𝑞𝑢𝑎𝑡𝑖𝑜𝑛 𝑜𝑝𝑒𝑟𝑎𝑡𝑒𝑠 𝑏𝑦 𝑎𝑠𝑠𝑢𝑚𝑖𝑛𝑔 𝑡ℎ𝑎𝑡 𝑡ℎ𝑒 𝑛𝑒𝑥𝑡 𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑙𝑢𝑒 𝑡𝑜 𝑜𝑐𝑐𝑢𝑟
𝑤𝑖𝑙𝑙 𝑏𝑒 𝑠𝑎𝑚𝑒 𝑎𝑠 𝑡ℎ𝑒 𝑐𝑢𝑟𝑟𝑒𝑛𝑡 𝑠𝑎𝑚𝑝𝑙𝑒 𝑣𝑎𝑙𝑢𝑒
𝐺( 𝑘𝑇𝑠 ) = 𝑔((𝑘 − 1) ) 𝑇𝑠
Delta modulation generates a staircase approximation to the input analogue waveform, at
each time interval the quantized waveform amplitude can increase or decrease by a fixed
amount of Δ.

3. JunaidMalik,
DT008/2, GroupA
In a (PCM) Pulse Code Modulation system, after sampling the signal, each sample of the
signal is quantized separately using a scalar quantize. This means that the samples before it
have no effect on the quantization process of the new samples. However when a band
limited random process is sampled at the Nyquist rate or at a faster rate, then the sampled
values are usually correlated random variables. The exception is when the previous
Samples give some information about the next sample, and this information can be
employed to improve the performance of the PCM system. For example, if the previous
sample value was small, with a high probability the next sample value will be small as well,
so it is not necessary to quantize a wide range of values to achieve a good performance.
Figure 1: Block diagram of Delta Modulation system
This is a simple block diagram of a delta modulation system. A major advantage of delta
modulation is the very simple structure of the system.
Figure 2 from this graph we can see a large delta and granular noise

4. JunaidMalik,
DT008/2, GroupA
Figure 3: Reference (3) from this graph we can see granular noise and a large slope overload
distortiondue to the small delta

5. JunaidMalik,
DT008/2, GroupA
Method:
In this laboratory we validated our design of the delta modulation systemusing Pspice and
obtained results with transient analysis.
In deltamodulationastaircase approximationis generatedateachtime interval.
The predictionerrorisgivenbythe followingequation:
𝜖( 𝑘𝑇𝑠) = 𝑔( 𝑘𝑇𝑠) − 𝑔′(𝑘𝑇𝑠)
Andthe quantizedpredictionerrorisgivenby:
𝜖 𝑞 ( 𝑘𝑇𝑠) = ∆𝑠𝑔𝑛[𝜖(𝑘𝑇𝑠)
At the receiver the sampled waveform is then reconstructed by:
𝑔( 𝑘𝑇𝑠) = 𝑔′(𝑘𝑇𝑠) + 𝜖 𝑞 ( 𝑘𝑇𝑠)
= 𝑔((𝑘 − 1)𝑇𝑠) ± ∆
A reconstruction filter recovers the analogue waveform g(t) from the reconstructed
waveform signal g( 𝑘𝑇𝑠)
The two typed of quantization errors that we came across were, slope overload distortion
and granular noise.
To avoid slope overload distortion we used the following equation:
𝛿
𝑇𝑠
≥ max [
𝑑𝑔( 𝑡)
𝑑𝑡
]
We avoided slope overload distortion by using a large value for ∆ or by using a small value
for 𝑇𝑠
In this lab we also encountered granular noise which occurs when we increased the step
size ∆, relative to the slope of the input waveform signal.
The waveform that resulted was a square wave with a period half that of the sampling
period.
We have observed that too large a step size causes granular noise and too small step size
results in slope-overload distortion. This means that a good choice for is a “medium” value,
but in some cases the performance of the best medium value (i.e., the one minimizing the

6. JunaidMalik,
DT008/2, GroupA
mean-squared distortion) is not satisfactory. An approach that works well in these cases is
to change the step size according to changes in the input. If the input tends to change
rapidly, the step size is chosen to be large such that the output can follow the input quickly
and no slope-overload distortion results.
If we assume thatwe have a sine wave inputof 1kHz givenby:
𝑔( 𝑡) = 𝐴𝑠𝑖𝑛(2𝜋𝑓𝑡)
The maximum slope of the signal g(t) is given by:
𝑑𝑔( 𝑡)
𝑑𝑡
= −cos(2𝜋𝑓𝑡)
= −2𝜋𝑓𝑐𝑜𝑠(2𝜋𝑓𝑡)
𝑑𝑔( 𝑡)
𝑑𝑡
= 2𝜋𝑓𝐴
= 6.28 × 103 × 𝐴
A ≤
103 𝑣/𝑠
6.28 × 103
𝐴 ≤
1
6.28
𝐴 ≤ 0.159 𝑣
This 0.159v is to avoid slope overload distortion.
So therefore we had to design ∆ , 𝑇𝑠 , A and F, such that slope overload distortion did not
arise in our simulation.

7. JunaidMalik,
DT008/2, GroupA
Schematic Designs:
Schematic Design 1
In the above circuit there is no op-amp action as the op-amp is connected to ground.
The op-amp output po(t) is equal to the op-amp input p(t)
𝑃𝑜( 𝑡) = 𝑝(𝑡)
Therefore in the above circuit the transistor is being driven by the second op-amp.
The op-amp amplifies the difference. The second op-amp is a comparator when g’(t)>g(t),
Vo = +Vs => Transistor switches on.
The integrator sums the plus and minus pulses to produce the staircase output g’(t)
G’(t) = ∑Po(t)
R2
1k
R3
1k
R5
5.6k
U1
OPAMP
+
-
OUT
U2
OPAMP
+
-
OUT
R6
33k
C1
0.22u
0
0
R7
100k
Q1
40242
V1
FREQ = 1000
VAMPL = 0.159v
VOFF = 0
V2
TD = 0
TF = 50ms
PW = 10u
PER = 100u
V1 = 5
TR = 50ms
V2 = 0
0
0
Junaid Malik and Aysha Shah Lab 5: Delta Modulation, 14//11/12

8. JunaidMalik,
DT008/2, GroupA
Schematic Design 2
SINEWAVE DELTA MODULATION
Thiscircuitwas usedto produce a sine wave.
R2
1k
R5
5.6k
U2
OPAMP
+
-
OUT
gt2
gt
0
0
R7
100k
pt
V1
FREQ = 1k
VAMPL = 0.159v
VOFF = 0
V2
TD = 0
TF = 50ns
PW = 10u
PER = 100u
V1 = 0
TR = 50ns
V2 = 0.1
0
0
U3A
CD4016B
IN
1
OUT
2
VC
13
VDD
14
VSS
7
V3
10Vdc
Junaid Malik and Aysha Shah Lab 5: Delta Modulation, 14//11/12
0
pot
0
R1
1k
C1
0.22u
U4
OPAMP
+
-
OUT

9. JunaidMalik,
DT008/2, GroupA
Schematic Design 3
SQUARE WAVEDELTA MODULATION
In the above circuitwe replacedthe transistorwithananalogue switchtoimprove the overall
performance of the deltamodulationsystem.
The sine wave amplitude A isrequiredtocause oravoidslope overloaddistortion.
The deignvalueswere checkedviasimulation.
Δ= 0.1v and 𝑇𝑠 = 100 𝜇𝑠
0.1
100𝜇𝑠
= 1𝑚 ≤ (
𝑑𝑔( 𝑡)
𝑑𝑡
)
𝑔( 𝑡) = 𝐴𝑠𝑖𝑛(2𝜋𝑓𝑡)
1𝑚 = 𝐴𝑠𝑖𝑛(2𝜋 × 1 × 103)
1𝑚 = 𝐴
U1
OPAMP
+
-
OUT
U2
OPAMP
+
-
OUT
R1
1k
R2
1k
R3
100k
R4
5.6k
R5
33k
pt
C1
0.22u
gt2
gt
0
V1
TD = 0
TF = 50ns
PW = 5us
PER = 50us
V1 = 0
TR = 50ns
V2 = 0.1
0
0
U3A
CD4016B
IN
1
OUT
2
VC
13
VDD
14
VSS
7
00
0
V3
10Vdc
pot
V4
TD = 0
TF = 50ns
PW = 0.5ms
PER = 1ms
V1 = 0
TR = 50ns
V2 = 0.1
V
V
V
V
Junaid Malik and Aysha Shah Lab 5: Delta Modulation, 14//11/12

10. JunaidMalik,
DT008/2, GroupA
Results
SINE WAVE DELTA MODULATION WITH ANALOGUE SWITCH
Thisis the samplingof the sine wave.
Time
5.0ms 5.5ms 6.0ms 6.5ms 7.0ms 7.5ms 8.0ms 8.5ms 9.0ms 9.5ms 10.0ms
V(PT)
0V
50mV
100mV
V(GT)
-200mV
0V
200mV
V(GT2)
-6.0mV
-5.0mV
-4.0mV
-3.0mV
SEL>>

11. JunaidMalik,
DT008/2, GroupA
SQUARE WAVE DELTA MODULATION WITH ANALOGUE SWITCH
The samplingof the square wave wasmore problematicthanthe sine wave insimulationasextreme
valueswere requiredof
𝑑𝑔
𝑑𝑡
inthe designingof the deltamodulationsystem.
𝑇𝑠 = 100𝜇𝑠 Δ = 100mv
𝛥
𝑇𝑠
= 1000v/s
Time
5.0ms 5.5ms 6.0ms 6.5ms 7.0ms 7.5ms 8.0ms 8.5ms 9.0ms 9.5ms 10.0ms
V(PT)
0V
50mV
100mV
V(GT2)
-200uV
0V
200uV
400uV
V(GT)
0V
50mV
100mV
SEL>>

12. JunaidMalik,
DT008/2, GroupA
Conclusion:
To summarise in practice from this lab I learned that we do not use a small Δ to minimise
the greater noise and a small 𝑇𝑠 to avoid slope overload distortion.
I learned that in Delta modulation there is two unique features, a 1-bit word which
eliminates the need for word framing and in simplicity in the hardware and algorithm
structure of the system. This means that there is no synchronization required as there is
only a one bit word used and the circuitry of the system is simplified.
I have observed that when a too large a step size is used it causes granular noise and when a
too small step size is used it results in slope-overload distortion. This means that a good
choice for Δ is a ‘medium’ value and not a too large or too small value, but in some cases the
performance of the best medium value may not be satisfactory for the system design. An
approach that works well in these cases is to change the step size according to the changes
observed in the input. If the input happens to change rapidly, the step size is chosen to be
large such that the output can follow the input quickly and so no slope-overload distortion
occurs in result. When the input is more or less varying the step size is changed to a small
value to prevent granular noise.
A key element I learned from this lab was that engineering is not conducted by trial and
error. It is based upon design, approach and methodology. In actual practice design comes
first, and then it is validated by computer simulation.
Usually in a system, ∆ is adoptively adjusted so that when granular noise dominates we used
to a small ∆ and when slope overload distortion dominates we used a large ∆.
This is known as adaptive delta modulation (ADM). For this there is a greater cost as more
circuitry is required but overall there is a performance is achieved by this way.

13. JunaidMalik,
DT008/2, GroupA
References:
(1) Lecture Notes - by Mark Davis
(2) Communication SystemsEngineeringby John G. Proakis and Masoud Salehi
(3) http://nptel.iitm.ac.in/courses/Webcourse-contents/IIT-
KANPUR/Digi_Img_Pro/chapter_7/fig17.gif