# Discuss V3 = 2.5V and V4 = 1.25V.

Discuss the operation of weighted
resistor DAC circuit and R/2R DAC. Include figures and detailed explanation
with relevant applications.

A
digital to analog converter (DAC) is required to convert digital signals into
analog signals. A digital binary number is converted into an analog voltage or
current, giving an output voltage or current relative to the binary input. (Kuphaldt,
2000)

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Block diagram of a DAC.

Digital
to analog converters are used in many applications, one of the most common uses
is for audio, in telephones and mobile phones. Digital information is converted
into audio signals. It is also used for speakers when playing music, headphones
etc.

Another
common application is display devices, mobile phones, televisions, HMI’s (Human
Machine Interface) where colours and shades are generated from digital video
signals. (Futureelectronics.com,
2018)

A
weighted resistor digital to analog converter uses a circuit similar to the
inverting summing op-amp circuit but with different resistor values instead of
equal. In a 4 input circuit, there will be five resistors, RF, R1, R2, R3 and
R4. Resistors 1 to 4 set at multiple powers of two, R1 = R, R2 = 2R, R3 = 4R
and R4 = 8R. Thus giving each digital signal exactly half the effect on the
output as the signal before it. With 4 binary signals there is a potential of
16 different analog output voltages.

(ElProCus –
Electronic Projects for Engineering Students, 2018)

Using
the formula;

Where V1, V2, V3 and V4 are the binary inputs all equal
to 10V the analog output voltages can be calculated. (Kuphaldt, 2000)

Inputs

Output

V1

V2

V3

V4

0

0

0

0

0V

0

0

0

1

1.25V

0

0

1

0

2.5V

0

0

1

1

3.75V

0

1

0

0

5V

0

1

0

1

6.25V

0

1

1

0

7.5V

0

1

1

1

8.75V

1

0

0

0

10V

1

0

0

1

11.25V

1

0

1

0

12.5V

1

0

1

1

13.75V

1

1

0

0

15V

1

1

0

1

16.25V

1

1

1

0

17.5V

1

1

1

1

18.75V

From
the above table we can see V1 = 10V, V2 = 5V, V3 = 2.5V and V4 = 1.25V. Showing
that the combination of the four binary inputs in this circuit can give a range
of different values from 0V – 18.75V.

With the weighted resistor digital to analog converter,
as the amount of digital binary signals increase, the amount of resistors
increases, and also the value of the resistors. This means that with a high
amount of digital binary signals a large range of resistors is required, this
can also reduce the accuracy of the circuit. (ElProCus – Electronic Projects for
Engineering Students, 2018). An advantage of the circuit is the low amount of
resistors required compared to other DACs, as only one resistor is required in
each network.

The R/2R DAC is an
alternative converter to the binary weighted resistor DAC which uses fewer
unique resistor values. Instead it uses a repeating structure of resistor
values R and 2R. This allows the circuit to be produced easier than the binary
weighted resistor, especially if the amount of digital binary signals is a
large number as the resistors required would all either be R or 2R instead of
R, 2R, 4R, 8R etc. however it does mean that there is an extra resistor
required in each network. The R/2R resistor could even be constructed only
using one value of resistor if desired, 2R can be made with 2 x R in series, or
R can be made with 2 x 2R in parallel. (Kuphaldt, 2000)

(ElProCus –
Electronic Projects for Engineering Students, 2018)

Discuss operation of
successive approximation ADC using examples, figures and applications of each.

The successive approximation analog to digital converter
is made up of four sub-circuits, sample and hold amplifier (SHA), analog
comparator, digital to analog converter (DAC) and successive approximation
register (SAR). (Analog.com,
2018)

The circuit uses the SAR to count by trying all the
values of the bits starting with the most significant bit (MSB) and finishing
with the least significant bit (LSB) if the DAC output is larger than the
analog input, then the bit that it is counting is switched off, if the DAC
output is smaller than the analog input then that bit is left switched on and
it moves onto the next most significant bit. It continues this process until
all of the bits within the successive approximation register have been tested. (Analog.com,
2018)

Successive approximation
ADCs are used heavily for data-acquisition systems, and was also first utilised
in pulse code modulation systems in the 1940s. Pulse code modulation systems
are used in digital audio recording systems, voice mails, telephones, radios,
digital video recording systems. (ElProCus – Electronic Projects for
Engineering Students, 2018)  It is also
utilised in ultrasonic welding systems for visual displays, the power of the
system is digitally measured and converted to an analog output 0-10V, which can
then be monitored as a percentage where 0.1V = 1%.

The advantage of this circuits counting strategy is it
allows it to process the data quickly, allowing for faster results than other
analog to digital converters such as the digital ramp ADC circuit. This can be
seen by comparing the outputs of the successive approximation ADC and the
outputs of the digital ramp ADC circuit.

The higher the input analog voltage, the longer the time
is between updates. Whereas the smaller the input analog voltage the shorter

By comparing the outputs of the successive approximation
ADC it can be noted that the outputs all occur at regular intervals thus giving
faster results.

Successive