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EEEN313
Assignment 1
1. (30 marks points) You have been asked to design the hardware for DC power sup- ply. The system has an input voltage that can vary from 12V to 32V DC, and you need to create a converter with a constant DC output voltage of 48V in to a 10Ω load. You will be designing the hardware, you can assume a controller is designed to ensure you have a constant 48V output with varying input. This controller will output a PWM signal of 40kHz.
Next, find a MOSFET and a diode that will work for this build, list your consider- ations for selecting both switches, and calculate the losses for your switching power pole (include the datasheet for each switch in the appendix).
There is an option to switch at a lower switching frequency of 1kHz. How will this alter the losses in your system?
2. (20 marks points) Displayed in figure 1 is the switching voltages across a buck con- verter’s inductor (20mH) which has a switching frequency of 50kHz and an output current of 6A. It is just a screen grab to illustrate the switching, so doesn’t show the accurate duty cycle or voltage amplitudes.
Find the following:
1. Vin
2. Vout
3. ∆IL
4. Assuming the load had the ability to vary, what size load will make the converter enter discontinuous conduction mode?
5. What size capacitor would be required to have an output ripple of 1%?
Figure 1: Switching voltage across buck converter inductor
3. (20 marks points) A buck-boost converter can step up or down the input voltage...
Discuss why a buck converter, or boost converter still exist (advantages/disadvantages).
4. (5 marks points) Describe the difference between continuous and discontinuous con- duction mode.
5. (30 marks points) In this question, you will be looking at using feedback to keep a constant DC voltage on the output of a DC/DC converter with a varying DC input. A good example of this is charging a phone (constant 5V) with a 12V battery as a supply (which has a voltage that varies from ≈ 11V to 14V).
We will be using some control techniques which were covered in ECEN315, but as not everyone has done ECEN315, I will do my best to cover everything in a lecture (could also be a good refresher).
We will be controlling the buck converter from lab 3 (asynchronous buck converter), we will be using matlab/simulink to test our system, I have supplied you with the simulink model of the buck converter and you can add feedback and test the response. We also need a couple of equations to help us design our proportional-integral (PI) controller. Equation 1 shows the transfer function for a CCM buck converter in the Laplace domain (covered in a lecture).
Where:
vo is the output voltage
d is the duty cycle
Vin is the input voltage
L is the inductor
C is the output capacitor
r is the series resistance of the output capacitor
R is the load
We will use the following values for the buck converter:
vo = 5V
Vin = 11V to 14V
L = 4mH
C = 10uF
r = 0.02Ω
R = 100Ω
fSW = 30kHz
An op-amp implementation of a PI controller is shown in figure 2, you can see it looks suspiciously like an inverting amplifier (mixed with an integrator circuit). Hopefully some of you remember equation 2, the gain of an op-amp inverting amplifier circuit.
Where:
The controller adds a pole at the origin (integrator) and a zero at:
A proportional gain of:
A integral gain of:
Figure 2: Op-amp PI controller
You can use the matlab function tf([],[]) to create a transfer function for the buck
converter and your controller. For the controller, it might look something like this: Page 3
...
% compute the numerator parameter
Cont num = Rf*C
% compute the denominator parameter
Cont den = Ri*C
% create controller transfer function
Controller = tf([Cont num 1],[Cont den 0])
...
1. In matlab, create a bode plot of the buck converter’s transfer function (the matlab function bode() might be helpful. Also, in matlab’s home screen you can type“help”and the function you want to use and it will give you information about the function)
2. Using Rf , Ri and C, design a PI controller where the phase of the plant (buck converter transfer function) is not altered at the unity gain frequency (where the bode plot gain crosses 0dB) and the gain of the controller (Kp) is 0.1. You may assume that Ri = 10kΩ. In your answers, give the values for Rf , Ri and C and show the working in the appendix as well as a description of your design choices
3. Create a bode plot of the controlled plant on the same plot as the uncontrolled system
4. Add your controller to the simulink buck converter simulation (you can add the transfer function, you don’t need to include an op-amp circuit)
The Voltage Subtractor
The Subtractor also called a differential amplifier, uses both the inverting and noninverting inputs to produce an output signal which is the difference between the twoinput voltages V1 and V2 allowing one signal to be subtracted from another. Moreinputs can be added to be subtracted if required.
If resistances are equal (RR3 and RAR4) then the output voltage is as given and thevoltage gain is +1. If the input resistance are unequal the circuit becomes a differentialamplifier producing a negative output when V1 is higher than V2 and a positive outputwhen V1 is lower than V2.
The Voltage Subtractor Op-amp Circuit
