XII Standard Electronics Notes (Updated as per Amravati Board Pattern), 2010-11
A-D & D-A Converters
Chapter 6, Paper 2
Learn the Basics First!
1) Analog signal means a smooooooooothly or linearly varying electrical signal w.r.t. time. It has
infinite variations in a given unit of time. All physical or electrical quantities in Nature are analog
signals.
2) Digital signal means an abruptly or suddenly changing electrical quantity w.r.t. time. It has definite
variations in a given unit of time. It is always artificial.
3) Potential divider is a circuit of two or more resistors connected generally in series, having a voltage
source. The algebraic sum of voltage drops across each resistor is equal to voltage source.
4) Flip-flop is a semiconductor circuit. It is made up of logic gates. It has two stable states. It can store a
single bit (binary digit), in the form of memory.
5) Clock is a periodic waveform, particularly a square wave. It is basically used to synchronize digital
circuits. It may be symmetrical or asymmetrical.
6) Register is a group of flip-flops used to store or rotate the binary data. The shift register rotates the
bits for certain arithmetic operations. It is either shift left or shift right register.
7) Counter is made up of flip-flops. It is capable of counting the number of clock pulses applied to it. It
produces binary output in sequence. The total number of states produced by counter is denoted by M.
The letter M means modulus or MOD of counter.
Need for A/D & D/A conversion – in general, there are two types of electrical signals – the analog
signal and the digital signal. The linear electronics circuit like linear amplifier, transducers; generate such
signals, while the computers generate digital signals.
In analog signal, voltage level changes smoothly or linearly with respect to time, while in digital
signal voltage level changes abruptly or suddenly. Sometimes it is required to connect output of a
transducer to input of a digital circuit, like a digital display. If they are connected directly then the results
are quite unsatisfactory. Because the digital circuit cannot ‘understand’ the linear signals of transducer.
Hence, we will NOT get satisfactory digital output from the circuit.
a) Therefore, whenever we need to interface (connect) analog and digital circuits, we need to convert
either analog signal into proportional digital signal or vice versa. In this way, we need the A/D and
D/A conversion. Examples: A/D conversion is required is digital voltmeter, A/D and D/A
conversions, both, are required in temperature controller, A/D conversion is required in digital
recording system etc.
Digital to Analog Converters (DAC)
The process of converting digital signal into equivalent analog signal is called D/A conversion.
The electronics circuit, which does this process, is called D/A converter. The circuit has ‘n’ number of
digital data inputs with only one output. Basically, there are two types of D/A converter circuits:
Weighted resistors D/A converter circuit and Binary ladder or R–2R ladder D/A converter circuit.
Weighted resistors D/A converter – here an opamp is used as summing amplifier. There are four
resistors R, 2R, 4R and 8R at the input terminals of the
opamp with R as feedback resistor. The network of
resistors at the input terminal of opamp is called as
variable resistor network. The four inputs of the circuit
are D, C, B & A. Input D is at MSB and A is at LSB.
Here we shall connect 8V DC voltage as logic–1 level.
So we shall assume that 0 = 0V and 1 = 8V. Now the
working of the circuit is as follows. Since the circuit is
summing amplifier, its output is given by the
following equation –
B
A
D C
Vo   R. 



 R 2 R 4 R 8R 
Helpline for electronic students: www.dsvidyasagar.com, Email: [email protected]
XII Standard Electronics Notes (Updated as per Amravati Board Pattern), 2010-11
35
Working – when input DCBA = 0000, then putting these value in equation (1) we get –
0
0
0 
0
Vo   R. 


  0V
 R 2 R 4 R 8R 
When digital input of the circuit DCBA = 0001, then putting these
value in equation (1) we get –
0
0 8V 
8V
0
Vo  R . 


 1V
   R.
8R
 R 2R 4R 8R 
When digital input of the circuit DCBA = 0010, then putting these
value in equation (1) we get –
0 8V 0 
8V
0
Vo   R. 


 2V
  R .
4R
 R 2R 4R 8R 
When digital input of the circuit DCBA = 0011, then putting these
value in equation (1) we get –
0 8V 8V 
0
 8V 8V 
Vo  R . 



   R.
  3V
 R 2R 4R 8R 
 4 R 8R 
In this way, when digital input changes from 0000 to 1111 (in BCD
Digital inputs
Analog output
D C B A
Voltage (Va)
0
0
0
0
0
0
0
0
1
1
1
1
1
1
1
1
0
0
0
0
1
1
1
1
0
0
0
0
1
1
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
0
1
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
0
1
style), output voltage (Vo) changes proportionally. This is given in the
conversion chart. There are some main disadvantages of the circuit.
They are –
1) Each resistor in the circuit has different value.
2) So error in value of each resistor adds up.
3) The value of resistor at MSB is the lowest. Hence, it draws more current.
4) Also, its heat & power dissipation is very high.
5) There is the problem of impedance matching due to different values of resistors.
0V
–1V
–2V
–3V
–4V
–5V
–6V
–7V
–8V
–9V
–10V
–11V
–12V
–13V
–14V
–15V
R–2R ladder D/A converter – it is modern type of resistor network. It has only two values of resistors
the R and 2R. These values repeat
throughout in the circuit. THE OPAMP IS USED
AT OUTPUT FOR SCALING THE OUTPUT
VOLTAGE.
The working of the circuit can be
understood as follows. For simplicity, we
ignore the opamp in the above circuit (this is
because its gain is unity). Now consider the
circuit, without opamp. Suppose the digital
input is DCBA = 1000. Then the circuit is
reduced to a small circuit. Its output is given
by –
V
 2R 
output  
   V  
2
 2R  2R 
Now suppose digital input of the same circuit
is changed to DCBA = 0100. Then the output
voltage will be V/4, when DCBA = 0010,
output voltage will be V/8, for DCBA = 0001, output voltage will be V/16 and so on. The general formula
for the above circuit of R–2R ladder, including the opamp also, will be –
C
B
A 
 D
Vo   R  




 2 R 4 R 8R 16R 
Solving the equation, we finally get –
V V V V 
Vo      
 2 4 8 16 
With the help of this formula, we can calculate any combination of digital input into its
equivalent analog voltage at the output terminals.
Helpline for electronic students: www.dsvidyasagar.com, Email: [email protected]
XII Standard Electronics Notes (Updated as per Amravati Board Pattern), 2010-11
36
Analog to Digital Converters (ADC)
The process of converting analog signal into equivalent digital signal is called A/D conversion.
The electronics circuit, which does this process, is called A/D converter. The circuit has only one input
with ‘n’ number of digital outputs. The basic idea of this process is given below –
Simultaneous A/D converter – a comparator compares the unknown voltage with a known value of
voltage and then produces proportional output (i.e. it will produce
either a 1 or a 0). This principle is basically used in the above
circuit. Here three comparators are used. Each has two inputs. One
input of each comparator is connected to analog input voltage. The
other input terminals are connected to fixed reference voltage like
+3/4V, +V/2 and +V/4. Now the circuit can convert analog voltage
into equivalent digital signal. Since the analog output voltage is
connected in parallel to all the comparators, the circuit is also
called as parallel A/D converter.
Working – Here each comparator is connected to a reference voltage of +3/4V, +V/2 and +V/4 with their
outputs as C3C2C1 respectively. Now suppose the analog input voltage change from 0 – 4V, then the
actual values of reference voltages will be +3/4V = 3V, +V/2 =2V and +V/4 =1V. Now there will be
following conditions of outputs of the circuit –
1) When input voltage is between 0 and 1V, the output will be C3C2C1 = 000.
2) When input voltage > 1V  2V, the output will be C3C2C1 = 001.
3) When input voltage > 2V  3V, the output will be C3C2C1 = 011.
4) When input voltage > 3V  4V, the output will be C3C2C1 = 111.
In this way, the circuit can convert the analog input voltage into its equivalent or proportional
binary number in digital style.
Counter type A/D converter – here one input of comparator is connected to the analog signal (i.e.
unknown voltage) and other is connected to the analog
output of binary ladder (R–2R ladder, at point ‘P’).
The clock–input block produces square waves. They
are connected to the gate–control block. When output
of comparator is HIGH (logic–1), it connects the clock
pulses to the input of counter. However, when its
output is LOW (logic–0), it cuts off the clock pulses,
so that counting stops. The number of clock pulses
connected depends on the value of analog voltage. The
higher is the analog voltage the greater is the number of clock pulses counted by the counter. Then
counter produces proportional binary output. Its output is fed to the level amplifier. It amplifies the output
voltage of counter proportionally. This output is then fed to binary ladder. The binary ladder produces
proportional analog voltage at point ‘P’.
Now when then circuit is switched on, initially the counter is RESET to 0000. Suppose we
connect a known value of analog voltage = 9V. Therefore, there will be a difference in input voltages of
comparator. Hence, output of comparator will be HIGH (logic–1). The counter will start counting the
clock pulses and will produce equivalent binary number. Its output will sequentially change from 0001,
0010, 0011 and so on. When the output is 1001, which is = 9V, both inputs of comparator will be at same
voltage. Therefore, its output will be LOW (logic–0). So the gate will be cutoff and the counter will stop
counting. The final digital output will be 1001 = 9V. In this way, any analog voltage can be converted
into its equivalent digital output.
Helpline for electronic students: www.dsvidyasagar.com, Email: [email protected]
XII Standard Electronics Notes (Updated as per Amravati Board Pattern), 2010-11
37
Successive Approximation Method – the basic drawback of counter method (given above) is that it
has longer conversion time. Because it always starts from
0000 at every measurement, until the analog voltage is
matched. This drawback is removed in successive
approximation method. In the adjacent figure, the method
of successive approximation technique is shown. When
unknown voltage (Va) is applied, the circuit starts up
from 0000, as shown above. The output of SAR advances
with each MSB. The output of SAR does not increase
step–by–step in BCD bus pattern, but individual bit
becomes high–starting from MSB. Then by comparison,
the bit is fixed or removed. Thus, it sets first MSB (1000),
then the second MSB (0100) and so on. Every time, the
output of SAR is converted to equivalent analog voltage
by binary ladder. It is then compared with applied
unknown voltage (Va). The comparison process goes on, in binary search style, until the binary equivalent
of analog voltage is obtained. In this way following steps are carried out during conversion –
1)
2)
3)
4)
5)
The unknown analog voltage (Va) is applied.
Starts up from 0000 and sets up first MSB 1000.
If Va  1000, the first MSB is fixed.
If Va < 1000, the first MSB is removed and second MSB is set.
The fixing and removing the MSBs continues upto last bit (LSB), until equivalent binary output
is obtained. The block diagram of successive approximation A/D converter is given below –
Solved Problems
Problem 1: Calculate the full-scale output voltage of a 5 bit binary ladder, if we consider the two logic
levels as 1 = 20V and 0 = 0V. Ans: –19.375V
Problem 2: Below given is the circuit of binary ladder, with applied digital signals (4–bit). Calculate the
analog output voltage at the given input combination, if 0 = 0V and 1 = 16V. Ans: –10V
Problem 3: Find all the possible output voltages of a weighted resistors D/A converter circuit, if 0 = 0V
and 1 = 6V. Draw the necessary circuit diagram also.
The End
Helpline for electronic students: www.dsvidyasagar.com, Email: [email protected]