Chapter 7 – DELTA MODULATOR
7-1: Curriculum Objectives
1.
To understand the theory of delta modulation.
2.
To understand the signal waveforms of delta modulation.
3.
Design and implementation of delta modulator.
4.
Measurement and adjustment of delta modulator.
7-2: Curriculum Theory
1. The Operation Theory of Delta Modulation
Delta modulation is a kind of source coding which can convert the analog signal to digital signal.
After that we can deal with the digital signal easily such as encoding, filt ering t he unwanted sig na l and so on. Furthermore, the transmission quality of digital signal is better than analog signal, this is because digital signal can recover the original signal easily by the comparator.
The block diagram of delta modulator is shown in figure 7-1. From figure 7-1, the subtraction between the low frequency signal x(t) and the signal x s
(t) will produce a difference signa l d(t) , where x s
(t) is a reference signal, which is the former sampling value. Therefore the expression of the difference signal d(t) is given as
However the difference signal d(t) will be converted by a limiter, then we can obtain a signal Δ(t) given as

Figure 7-1 Block diagram of delta modulator.
Hence, we know that if the difference signal d(t) is larger than zero, this means that the reference signal x s
(t) is lower than the low frequency signal x(t), i.e. the estimated value is too small and we need to increase the next estimated value by Δ, on the other words, we only need to send a variation value, which is Δ during the transmission. Nevertheless, if the difference signal d(t) is lower than zero, then we only need to transmit a variation value, which is - Δ.
Thus it can be seen that every sampling value is related to the former sampling value, therefore, we can estimate the next sampling value base on the former sampling value. Then we only need to concentrate on the t rans mis s io n o f t he estimat ed va lue and need no t care abo ut t he quantification encode, so this situation can greatly save the transmission bandwidth. As for PCM modulation, every sampling value is independently and need to be quantified for encoding, thus, this situation will increase transmission bandwidth. For example, if the PCM signal after encoded is 8 bits, then the transmission bandwidth will be B
T
≥ 8f s
/ 2 = 4f s
= 8 W , which is 8 times more than the original bandwidth. Alt hough PCM modulation increases the quality of transmission, it also increases the transmissio n bandwidth. However delta modulation can reduce the transmission bandwidth and achieve the quality of transmission as PCM modulation.

Assume the sampling signal be
After the signal Δ(t) is sampled, we can obtain the expression of delta modulation signal as
Finally we integrate the delta modulation signal to take as the next reference signal x, (t) of delta modulation signal. The expression is given as
Although delta modulation has the advantages of simple structure and small transmission bandwidth, it also has the disadvantage of slope overload. As a result of delta modulation is the capacity of the variation Δ in the T, region, therefore the maximum slope of the delta modulation is Δ / T, = f Δ. If the maximum slope of the input signal exceeds Δ / T, = f s
Δ, that means the step size is too small, then slope overload will occur in the delta modulation. Consequently the slope of the input signal must satisfies the prerequisite condition of delta modulation, which is given as follow
Slope overload will cause the modulation signal changes cannot follow closely enough to the input signal, and then the recovery of the original signal will become distorted. In order to prevent slope overload, we notice that from equation (7-6), the slope of the input signal cannot be too high and we can also increase the values of f s
or Δ.

2. Implementation of Delta Modulator
Figure 7-2 is the basic circuit diagram of delta modulation. The audio signal will pass through a lowpass filter to remove the unwanted signals, which can prevent the interference from noise. The comparator is to compare the audio signal and the output signal of integrator, then the difference will be sampled by the D-type flip-flop and the output signal is a TTL digital signal. After that the output signal will feedback to integrator for integration and the output signal of integrator will again compare to the input signal to obtain the value of Δ or – Δ.
We modified the circuit diagram of delta modulation in figure 7-2 to figure 7-3. From figure 7-3, we add a multiplexer to control the gain of the integrator. This is because the gain of the integrator will affect the slope of the output signal of integrator, therefore, this method can prevent the occurrence from slope overload. U1 is the comparator, which can compare the audio signal and the output signal of integrator, then the output square wave signal will be sampled by a D-type flip-flop and finally the output signal is the delta modulation signal. U2 is the conversion of unipolar to bipolar circuit. Since there is no output signal from integrator by inputting the unipolar square wave signal, therefore, we need to convert the unipolar signal to bipolar signal. Analog switch is a structure of multiplexer. The purpose of the analog switch is the selection of the amplified gain of integrator. When AB=00, the signal will pass through R
1 4
, R
1 3
, R
12
, R
11
and send into integrator; when AB= 11, the signal will pass through R
14 to integrator. U3 is an inverse integrator.
The expression without R
16 is given as
By adding a shunt resistor R
16
between integrator U3 and capacitor C
1
, we can improve the low frequency response of the integrator. Assume that R
16
and C
1
are equivalent impedance, then we get

where
Figure 7-2 Basic circuit diagram of delta modulator.

Figure 7-3 Circuit diagram of delta modulator.

7-3: Experiment Items
Experiment 1: Delta modulator
1.
To implement a delta modulator circuit as shown in figure 7-3 or refer to figure DCT7-1 on
GOTT DCT-6000-04 module.
2.
Let J2 and J3 be short circuit, i.e. the connection between X
0
and X is on. At the signal input port (I/P1), input a 2 V amplitude and 500 Hz sine wave frequency. Next at the CLK input port
(I/P2), input a 5 V amplitude and 32 kHz TTL signal. Then observe the input signal (T1), the output port of comparator (T2), the output port of the conversion from unipolar to bipolar (T3), the output port of tunable gain (T4), the output port of integrator (T5) and the output port of delta modulation signal (O/P) by using oscilloscope. Finally record the measured results in table
7-1.
3.
According to the input signals in table 7-1, repeat step 2 and record the measured results in table
7-1.
4.
Let J2 and J4 be short circuit, i.e. the connection between X
1
and X is on. At the signal input port (I/P1), input a 2 V amplitude and 1 kHz sine wave frequency. Next at the CLK input port
(I/P2), input a 5 V amplitude and 64 kHz TTL signal. Then by using oscilloscope, observe on the output signal waveforms of T1, T2, T3, T4, T5 and O/P signal. Finally record the measured results in table 7-2.
5.
According to the input signals in table 7-2, repeat step 4 and record the measured results in table
7-2.
6.
Let J1 and J3 be short circuit, i.e. the connection between X
2 and X ison. At the signal input port
(I/P1), input a 2 V amplitude and 1.5 kHz sine wave frequency. Next at the CLK input port (I/P2), input a 5 V amplitude and 128 kHz TTL signal. Then by using oscilloscope, observe on the

output signal waveforms of T1, T2, T3, T4, T5 and O/P signal. Finally record the measured results in table 7-3.
7.
According to the input signals in table 7-3, repeat step 6 and record the measured results in table
7-3.
8.
Let J1 and J4 be short circuit, i.e. the connection between X
3 and X ison. At the signal input port
(I/P1), input a 2 V amplitude and 2 kHz sine wave frequency. Next at the CLK input port (I/P2), input a 5 V amplitude and 256 kHz TTL signal. Then by using oscilloscope, observe on the output signal waveforms of T1, T2, T3, T4, T5 and O/P signal. Finally record the measured results in table 7-4.
9.
According to the input signals in table 7-4, repeat step 8 and record the measured results in table
7-4.

7-4: Measured Results
Table 7-1 Measured results of delta modulation with 32 kHz CLK signal.
Input Signals Measured Results
500 Hz
2V
T1
T3
T2
T4
T5 DM O/P

Table 7-1 Measured results of delta modulation with 32 kHz CLK signal (Continue).
Input Signals Measured Results
1 kHz
2V
T1
T3
T2
T4
T5 DM O/P

Table 7-1 Measured results of delta modulation with 32 kHz CLK signal (Continue).
Input Signals Measured Results
2 kHz
2 V
T1
T3
T5
T2
T4
T6

Table 7-1 Measured results of delta modulation with 32 kHz CLK signal (Continue).
Input Signals Measured Results
3 kHz
2V
T1
T3
T2
T4
T5 DM O/P

Table 7-2 Measured results of delta modulation with 64 kHz CLK signal.
Input Signals Measured Results
1 kHz
2V
T1
T3
T5
T2
T4
DM O/P

Table 7-2 Measured results of delta modulation with 64 kHz CLK signal (Continue).
Input Signals Measured Results
2 kHz
2 V
T1
T3
T5
T2
T4
DM O/P

3 kHz
2 V
Table 7-2 Measured results of modulation with 64 kHz CLK signal (Continue).
Input Signals Measured Results
T1
T5
T3
T2
T4
DM O/P

Table 7-2 Measured results of delta modulation with 64 kHz CLK signal (Continue).
Input Signals Measured Results
T2
4 kHz
2 V
T1
T3 T4
T5 DM O/P

1.5 kHz
2 V
Table 7-3 Measured results of delta modulation with 128 kHz CLK signal.
Input Signals Measured Results
T1
T5
T3
T2
T4
DM O/P

Table 7-3 Measured results of delta modulation with 128 kHz CLK signal (Continue).
Input Signals Measured Results
T2
3 kHz
2 V
T1
T3 T4
T5 DM O/P

Table 7-3 Measured results of delta modulation with 128 kHz CLK signal (Continue).
Input Signals Measured Results
T2
5 kHz
2 V
T1
T3 T4
T5 DM O/P

Table 7-3 Measured results of delta modulation with 128 kHz CLK signal (Continue).
Input Signals Measured Results
T2
7 kHz
2 V
T1
T3 T4
T5 DM O/P

2 kHz
2 V
Table 7-4 Measured results of delta modulation with 256 kHz CLK signal.
Input Signals Measured Results
T1
T5
T3
T2
T4
DM O/P

Table 7-4 Measured results of delta modulation with 256 kHz CLK signal (Continue).
Input Signals Measured Results
T2
4 kHz
2 V
T1
T3 T4
T5 DM O/P

Table 7-4 Measured result of delta modulation with 256 kHz CLK signal (Continue).
Input Signals Measured Results
6 kHz
2 V
T1
T3
T5
T2
T4
DM O/P

Table 7-4 Measured results of delta modulation with 256 kHz CLK signal (Continue).
Input Signals Measured Results
8 kHz
2 V
T1
T3
T5
T2
T4
DM O/P

7-5: Problems Discussion
1.
Try to sketch the block diagram of delta modulation.
2.
Explain the purposes of comparator and conversion of unipolar to bipolar in figure 7-2.
Why?
3.
Explain the purposes of analog switch in figure 7-3.
4.
If the signal of CLK in figure 7-3 is not TTL signal, then describe what will the outputbe.