Electrical and Control Systems: Assignment Two - Analysis & Design

This assignment solution provides a comprehensive analysis of several key electrical engineering concepts. It begins with a detailed discussion of Digital-to-Analog Converter (DAC) circuits, including weighted resistor DACs and R/2R DACs, along with their operations, advantages, disadvantages, and applications. The solution then explores successive approximation Analog-to-Digital Converters (ADCs), explaining their working principles, advantages, disadvantages, and applications. The document further delves into the operation and modes of a sample and hold circuit amplifier, explaining terms such as acquisition time, aperture time, and drift time. Finally, the assignment addresses PID controllers, including their use in improving system responses, with a focus on a system with a given transfer function, and involves calculations, comparisons, and Matlab-based response plots to illustrate the effects of different control strategies. The solution includes relevant figures, equations, and references.

Electrical and Control 1
ASSIGNMENT TWO
Students name
Electrical and Electronic control
Tutors name
Institutions name
City and state
13/01/2018

Electrical and Control 2
TASK 1
Discuss the operation of weighted resistor DAC circuit and R/2R DAC. Include figures and
detailed explanation with relevant applications.
1. Weighted resistor DAC
The figure above shows a 4-digit code binary weighted resistor with an op amp connected in
the inverting mode. The weighted resistors are used to distinguish bits in terms of their
significance. Transistors are used to switch between the ground and reference voltage. The op-
amp is used to convert the current to voltage. The above 4-bit converter has 16 combinations

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of outputs which is given by 24=16. The binary inputs are simulated by the 4 switches from b0-
b3.
OPERATION
I. Switch Bo closed
The circuit would be supplied directly by the +5V, making it the value of voltage across R.
Current passing through it would be given by 5 V
10 KΩ = 0.5mA. Considering that the input bias
current is negligible, the current through the feedback resistor (Rf) remains 0.5mA and the
output voltage
V o= -1KΩ×0.5mA=-1.5V
II. B0 is open, b1 is closed
+5V supply would be connected to R/2. Current through R would be double the amount that
goes through Rf =1mA, which also doubles the amount of output voltage (Ian A, 2005).
III. Close both b0 and b1
1.5mA= current through Rf
Vo =1.5mA×-1kΩ=-1.5V
From above calculations, it is seen that the binary weighted currents are attained from the
input resistors depending on the state of the switches b0-b3 (ON/0FF) (Kal, 2009) The sum of
the obtained currents passes through Rf which is then converted to an appropriate voltage
value. This method can be summed as follows: Vo= -Rf× ([ b 0
R ] [ b 1
R /2] [ b 2
R /4 ] [ b 3
R /8 ]) where the
inputs can either be LOW(0V) or HIGH(+5V).
Disadvantages of using the above method is as follows;

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1. The resistance ratio is not easy to maintain when the binary inputs increase in number
(Kishore, 2009).
2. The wattage ratings of the resistors are different because of the difference in current
through them.
3. Larger values of resistance are more prone to error.
4. Likewise, large resistors are not cost friendly.
2. R/2R
This type of ladder DAC is made with a spilt structure of resistors with values R and 2R. This
is necessary to increase level of precision because of the ease of coming up with valued
matched current sources. The figure below shows a R-2R DAC converter.

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The bits correspond to specific switches. When the bit is low(0V) the switch is connected to
ground but if the switch is high (+5V) then the switch is connected to the op-amps inverting
input (U.A.Bakshi, 2009).
The value of the equivalent resistor can be obtained as follows from the analysis of the
figure below, also considering that an ideal op-amp is used.
Req= ( 2 R ) (2 R)
(2 R+2 R) =R
Using nodal analysis, the values of the voltages (V1-V3) can be obtained as follows:
V 3= ( R
( R+ R))V 2 = 1
2 V 2
Similarly,
V3
2R2R
RR
V3V2

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V 2 = 1
2 V 1
V 1= 1
2 V ref
V out =−IR
Equating the voltages to V ref we obtain the following
V 3= 1
8 V ref
V 2= 1
4 V ref
V 1= 1
2 V ref
V out = -R [b3
V ref
2 R + b2
V ref
4 R +b1
V ref
8 R +b0
V ref
16 R ]
Where the values of the bits can either be a binary zero or a binary one.
For our 4-bit ladder the equation can be simplified as follows,
V out = -V ref [b3
1
2+ b2
1
4 +b1
1
8 +b0
1
16 ]
A general R-2R ladder output voltage can be calculated from the following the formula (Ukil,
2007).
V out =−V ref ∑
i =1
n
bn−1
1
2i
APPLICATIONS OF A DAC
DAC are used in many areas that involve digital signal processing. Here are some of the
applications

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Video encoder- analog video signals are produced from DACs that receive signals from the
video encoder. The outputs are then optimized (U.A.Bakshi, 2009).
Audio amplifier- microcontroller gains are usually used to produce DC voltage gain. These ICs
may have DACs integrated within their system as video encoders.
Motor control- most motors need voltage control systems. Considering the efficiency of a DAC
which can be controlled by a controller or processor.
Display electronics- the RGB colour on display screens is produced by a video DAC that receives
data signals sent by a graphic controller.
Discuss operation of successive approximation ADC using examples, figures and applications
of each.
Successive approximation ADC is used to increase speed of operation and reduce the
conversion (Akkinapally, 2006) . Unlike in the digital ramp type ADC with only one counter, this
one has it replaced by a successive approximation register (SAR). Depending on the input, the
register basically counts by shifting the bits from the MSB to LSB.
WORKING

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The DAC is capable of converting output analog signals from the SAR, which is then compared
with the Opamp comparators sampled input analog value (Luecke, 2005). The clock pulse
provided by the Opamp as high or low depends on the differences within the logic circuit. Given
a 3-bit SAR, in the first scenario the SAR allows its MSB as “1,” high making it “100”. The analog
equivalent is obtained and then compared with Vin, (input sampled voltage). Depending on the
difference of the two (if positive or negative) the SAR enables the next MSB making “110” the
result or the last set bit is reset and resultant output is “101”.
From this, the conversion rate of the 3-bit ADC will be 3 clock pulses. Hence 3 clock pulses
should end first before taking the next input sample signal.
Advantages
 The design is compact and cheap
 The ratio of speed to power is commendable
 Has a high speed compared to other types of ADC
Disadvantages
 The design is complex
 Successive approximation registers make it costly
Application
The successive approximation ADC is commonly used in techniques of data acquisition at rates
of above 10 KHz (U.A.Bakshi, 2009).
Task 2
a.) The diagram shows a typical sample and hold circuit amplifier explain circuit operation
and modes of operation of the circuit.

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A1 and A2 are voltage follower circuit amplifiers. The transistor is operated in ON and OFF
state. The operation of the transistor switch is facilitated by the sample control. The input signal
is supplied at Vin and is outputted by A1 because of its high input impedance. Upon application
of sample control, transistor switch is turned ON and conducting starts (Onwubolu, 2005). The
output impedance of both the amps is very small because of their 100% feedback. The (rdsON)
drain and source resistance also remains small. The capacitor now starts to charge due to A1s
output impedance and rdsON.
charging time constant =C ×rout × rdsON
Time taken is less because of the small values of rout and rdsON.
When the transistor switch is turned off, the capacitor detaches from the circuit and holds the
charge it had conducted. The time to discharge the capacitor becomes more because of the
high input impedance of A2 thus making it hold the charge for a period of time (Plassche, 2013).
With A2 having a gain of unity, the output voltage equals the charge stored by the capacitor.
b.) Explain the following terms based on the sample and hold command graph

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 Acquisition time – time required to charge the holding capacitor to a level almost similar
to the input voltage. it is dependent on the slew rate and maximum output current of
op-amp and RC time constant.
 Aperture time – time period describing the behaviour of the sample control circuit after
giving the hold command. Usually it is supposed to halt all operations when given the
hold signal but instead it still monitors changes in the input voltage for a short period of
time.
 Drift time- variation that exists on the aperture time between sampling periods
 Settling time- the time period used by the input voltage that charges the capacitor to
settle completely after the hold command is applied.
 Hold step- describes variance in output voltage caused by the unwanted charges that
transfer from the switch to the capacitor during the time of switching from hold to
sample or sample to hold.
 Turn-off time – refers to the amount of time it takes for the sample and hold circuit to
be turned ON and OFF during its operation (Plassche, 2012).
c.) If the ON resistance of T1 in the above figure is 30Ω and C1 is 1μF, Calculate the time
required for the capacitor voltage to reach a value within 1 percent of the input voltage.
Given charging time constant =C ×rout × rdsON
Time constant = 30Ω × 1μF ×1 = 30μS
Task 3
A PID controller is used to improve the overall response of a system. A system with Transfer
function (T.F) = (2S+9)/ (S2+2S+4) is given with a gain of 2.

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Change to values of P or I or D to improve the steady state response of the system. Clearly plot
the response on Matlab with Input and output graphs and submit along with your work.
Calculations must include most of the following:
 Compare the transfer function with second order system equation
 Stability
 Speed of response
 Methods of control e.g. PI, PD or PID and comparison of their performance
You are expected to specifically reference all equations to standard control system texts.
Bibliography
Akkinapally, S. S., 2006. Design and Implementation of 8 Bit Successive Approximation ADC at
1MHz. rhode Island : University of Rhode Island.
Ian A, G., 2005. Intergrated Circuit Test Engineering: Modern Techniques. London : Springer
Science+ Media .
Kal, S., 2009. BASIC ELECTRONICS: DEVICES, CIRCUITS AND IT FUNDAMENTALS. New Dheli:
Asoke K, Ghosh.
Kishore, K. L., 2009. Operational Amplifiers and Linear Integrated Circuits. India : Dorling
Kindersley .
Luecke, G., 2005. Analog and Digital Circuits for Electronic Control System Applications: Using
the TI MSP430 Microcontroller. second ed. London : Newnes .
Onwubolu, G., 2005. Mechatronics: Principles and Applications. First ed. Fiji : Elsevier.
Plassche, R. J. v. d., 2012. Integrated Analog-To-Digital and Digital-To-Analog Converters.
Second ed. New York : Springer Science & Business Media.

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Plassche, R. J. v. d., 2013. CMOS Integrated Analog-to-Digital and Digital-to-Analog Converters.
Second ed. New York : Springer Science & Business Media.
U.A.Bakshi, A., 2009. Analog Integrated Circuits - Design And Applications. Third Revised Edition
ed. Pune : Technical Publications Pune .
U.A.Bakshi, A., 2009. Linear Ic Applications. First ed. Pune : Technical Publications .
U.A.Bakshi, A., 2009. Power electronics - II. First Edition ed. Pune : Technical Publications Pune .
Ukil, A., 2007. Intelligent Systems and Signal Processing in Power Engineering. New York :
Springer Science & Media .