EECE 430
Lab 1: Pulse- Width Modulation (PWM) and Filter
Characteristics
Kellen Maria Kalema Naluwaga
10/4/2023
Objectives
Component and Equipment List
Analysis of Input voltage VA and the Output Voltage
Vo
Analysis of Input Source Characteristics
a. Pulse Width Change Analysis to 6us
b. Switching Frequency Change Analysis to
20kHz
c. Pulse width Change Analysis to 5us
Transfer function Analysis of Vo(s)/VA(s)
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Objectives
The main objective of the lab is centred around exploring and understanding the relationship and
behaviour of electrical circuits in response to pulse width modulation (PWM) and varying input
conditions. Through experiments with different PWM settings, AC input, and analyses like Fourier
and transfer functions, the lab delves into practical aspects of how circuit elements (L, C, and R)
respond to different frequencies and harmonic components, specifically focusing on transient
responses, resonance, and filtering characteristics. By simulating and/or physically measuring
parameters like voltage, current, and frequency under varying scenarios, the lab aims to deepen
understanding of circuit theory, electrical resonance, and filtering in practical, real-world applications.
Component and Equipment List
PSpice
Analysis of Input voltage VA and the Output Voltage Vo
Image showing built Buck Converter Circuit/LC low-pass filter
In the circuit configuration, where VA is the voltage across an inductor in series with a PWM voltage
source, and V0​is the voltage across a resistor and capacitor in parallel (placed in parallel to the PWM
voltage source), determining the exact moment when V0 reaches steady state will depend on Duty
Cycle. The average value of the PWM waveform, which influences the final steady-state value of V0
is determined by its duty cycle. A higher duty cycle would raise the average voltage and therefore the
steady-state value of V0.
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Image showing plot of the input voltage VA and the output voltage VO
Relation between VO and VA
Given VA​is the voltage applied across an inductor (L) in series with a PWM source, and V0 is the
voltage across a resistor (R) and capacitor (C) in parallel, which are in parallel with the PWM source,
VA is a Pulse Width Modulated (PWM) signal. The average voltage (Vaverage) across the inductor
due to the PWM can be calculated using the duty cycle (D) and high/low voltage levels (VH and VL)​
of the PWM:
VAavg =VL +D×(VH−VL). When the PWM signal is applied across the inductor, due to its property
to resist changes in current, the inductor will smooth out the variations in VA, creating a more DC-like
voltage (with some ripple) across it. The resistor (R) and capacitor (C) parallel combination forms a
low-pass filter. If the PWM frequency is sufficiently high, V0 will approximate the average DC value
of VA (VAavg), though with some ripple. The exact ripple and transient response characteristics
depend on the L and RC values, as well as the PWM frequency and duty cycle. In summary, under
steady-state conditions: V0 ≈VAavg
​
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No.3
VA Component
4
V0 Component
In a buck converter, the average of V0 (output voltage) should be approximately equal to the average
of VA (input PWM voltage) under steady-state conditions.
The fundamental frequency of a PWM signal is equal to its switching frequency. If you generate a
PWM signal with a period T, the fundamental frequency f1 is the inverse of this period: f1 = 1/T
​The resonance frequency ( fres) of an LC circuit is given by:
Fres = 1/ (2π sqrt(LC)) Where L is the inductance and C is the capacitance in the filter. The ratio of
the switching frequency fs to the LC resonance frequency can be expressed as: Ration= fs / fres
The attenuation of the fundamental frequency by the LC filter depends on the filter design and the
ratio of the switching frequency to the LC resonance frequency. The LC filter provides a low-pass
filtering effect, ideally allowing DC and low-frequency signals to pass while attenuating
high-frequency signals.
6 us Pulse width
The duty cycle (D) of the PWM signal is defined as the ratio of the pulse width (PW) to the period (T)
of the waveform. D = PW/ T . Changing PW from 6µs to 7.5µs, while keeping the period (T)
constant, will increase D, altering the average value of the PWM signal and hence the DC component
delivered to the load.
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Image showing plot of the input voltage 6us VA and the output voltage VO
Relation between VO and VA
Given VA​is the voltage applied across an inductor (L) in series with a PWM source, and V0 is the
voltage across a resistor (R) and capacitor (C) in parallel, which are in parallel with the PWM source,
VA is a Pulse Width Modulated (PWM) signal. The average voltage (Vaverage) across the inductor
due to the PWM can be calculated using the duty cycle (D) and high/low voltage levels (VH and VL)​
of the PWM:
VAavg =VL +D×(VH−VL). When the PWM signal is applied across the inductor, due to its property
to resist changes in current, the inductor will smooth out the variations in VA, creating a more DC-like
voltage (with some ripple) across it. The resistor (R) and capacitor (C) parallel combination forms a
low-pass filter. If the PWM frequency is sufficiently high, V0 will approximate the average DC value
of VA (VAavg), though with some ripple. The exact ripple and transient response characteristics
depend on the L and RC values, as well as the PWM frequency and duty cycle. In summary, under
steady-state conditions: V0 ≈VAavg
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6us VA Component
In a buck converter, the average of V0 (output voltage) should be approximately equal to the average
of VA (input PWM voltage) under steady-state conditions.
The fundamental frequency of a PWM signal is equal to its switching frequency. If you generate a
PWM signal with a period T, the fundamental frequency f1 is the inverse of this period: f1 = 1/T
​The resonance frequency ( fres) of an LC circuit is given by:
Fres = 1/ (2π sqrt(LC)) Where L is the inductance and C is the capacitance in the filter. The ratio of
the switching frequency fs to the LC resonance frequency can be expressed as: Ration= fs / fres
The attenuation of the fundamental frequency by the LC filter depends on the filter design and the
ratio of the switching frequency to the LC resonance frequency. The LC filter provides a low-pass
filtering effect, ideally allowing DC and low-frequency signals to pass while attenuating
high-frequency signals.
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6us VO Component
N0. 5 (Switching Frequency)
The fundamental frequency of the PWM signal now becomes 20kHz ensuring that the pulse width is
appropriate to maintain desired duty cycle values at the new frequency. The relationship between the
switching frequency and the LC filter (or other present filters') resonant frequency affects the output
voltage, ripple, and transient response. The increased simulation time allows the circuit to reach a
steady state, especially if the frequency changes have affected the transient response time. The Longer
simulations provide a more detailed look into slow-changing variables and low-frequency behaviours.
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Image showing plot of the input voltage 20kHz VA and the output voltage VO
Relation between VO and VA
Given VA​is the voltage applied across an inductor (L) in series with a PWM source, and V0 is the
voltage across a resistor (R) and capacitor (C) in parallel, which are in parallel with the PWM source,
VA is a Pulse Width Modulated (PWM) signal. The average voltage (Vaverage) across the inductor
due to the PWM can be calculated using the duty cycle (D) and high/low voltage levels (VH and VL)​
of the PWM:
VAavg =VL +D×(VH−VL). When the PWM signal is applied across the inductor, due to its property
to resist changes in current, the inductor will smooth out the variations in VA, creating a more DC-like
voltage (with some ripple) across it. The resistor (R) and capacitor (C) parallel combination forms a
low-pass filter. If the PWM frequency is sufficiently high, V0 will approximate the average DC value
of VA (VAavg), though with some ripple. The exact ripple and transient response characteristics
depend on the L and RC values, as well as the PWM frequency and duty cycle. In summary, under
steady-state conditions: V0 ≈VAavg
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20kHz VA Component
In a buck converter, the average of V0 (output voltage) should be approximately equal to the average
of VA (input PWM voltage) under steady-state conditions.
The fundamental frequency of a PWM signal is equal to its switching frequency. If you generate a
PWM signal with a period T, the fundamental frequency f1 is the inverse of this period: f1 = 1/T
​The resonance frequency ( fres) of an LC circuit is given by:
Fres = 1/ (2π sqrt(LC)) Where L is the inductance and C is the capacitance in the filter. The ratio of
the switching frequency fs to the LC resonance frequency can be expressed as: Ration= fs / fres
The attenuation of the fundamental frequency by the LC filter depends on the filter design and the
ratio of the switching frequency to the LC resonance frequency. The LC filter provides a low-pass
filtering effect, ideally allowing DC and low-frequency signals to pass while attenuating
high-frequency signals.
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20kHz V0 Component
NO. 6 (50% Duty Ratio)
A 50% duty cycle implies that the average voltage (Vavg) of the PWM signal will be half of the peak
voltage (assuming a symmetric waveform starting from zero). This could alter the DC level to which
capacitive and inductive elements charge. The transient response of LC and RC elements to the
change in PWM pulse width can result in over/undershoots, longer settling times, and altered peak
responses. The time constants associated with L, R, and C will determine how quickly the circuit
responds to changes, and this may be reflected in different inrush currents, dV/dt, and dI/dt during
transitions.
the amplitude of the fundamental frequency in the frequency domain (Fourier series) is calculated as
follows:
A1 = 4⋅Vpeak / π .
Here:
A1 is the amplitude of the fundamental frequency component.
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Vpeak is the peak voltage of the square wave.
If, for instance, you are switching between V1 =0V and V2 =10V, then
Vpeak will be 10V. Amplitude = (4*10)/pi = 12.73V
So, the amplitude of the fundamental frequency component of a 10V, 50% duty cycle wave is
approximately 12.73V. This is larger than the peak value of the time-domain signal due to the nature
of Fourier decomposition, where the square wave is represented as a sum of sine waves.
N0. 7 (Transfer Function Analysis)
Image showing plot of the input voltage VA and the output voltage VO from an
AC Voltage Component
When the pulse voltage input is replaced with an AC voltage input, the relationship between the
frequency at which the transfer function gain peaks and the LC resonance frequency can be analysed.
In a simple series LC circuit, resonance occurs when the inductive and capacitive reactances cancel
each other out. The transfer function describes the relationship between the input and output of a
linear time-invariant system in the frequency domain. The frequency at which the transfer function
gain peaks coincides with the LC resonance frequency because at this frequency, the impedance is
minimised (or maximised in a parallel LC circuit), allowing maximum current (or voltage in parallel
LC) to flow through the circuit.
NO. 8
The attenuation of the fundamental frequency depends on the specific circuit configuration and
components involved.
Attenuation, A in dB, is given A=20log10​(∣H(jω1​)∣). Note that a gain of less than 1 (or -dB) means
the signal is attenuated at this frequency.
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