Objectives:

The purpose of the lab is to investigate the frequency response of a passive filters and get the fundamentals on

circuit design and analysis in the frequency domain.

List of Equipment and components required:

1. Elvis II* Prototyping board

2. Digital Multimeter

3. Function generator

4. Oscilloscope

Network Analysis and Bode plots

5. Capacitors

6. Resistors

7. Jumper wires

Introduction

Frequency domain representation

The frequency response is a representation of the system's response to sinusoidal inputs at varying frequencies; it is

defined as the magnitude ratio and phase difference between the input and output signals. If the frequency of the

source in a circuit is used as a reference, it is possible to have a complete analysis in either the frequency domain or

the time domain. Frequency domain analysis is easier than time domain analysis because differential equations used

in time transforms are mapped into complex but linear equations that are function of the frequency variable s(jw). It

is important to obtain the frequency response of a circuit because we can predict its response to any other input.

Therefore, it allows us to understand a circuit's response to more complex inputs.

Filters are important blocks in communication and instrumentation systems. They are frequency selective circuits

and widely used in applications such as radio receivers, power supply circuits, noise reduction systems and so on.

There are four general types of filters depending on the frequency domain behavior of the transfer function

magnitude; Low-pass filters (LPF) that pass low frequency signals and reject high frequency components; Band-

pass filter (BPF) pass signals with frequencies between lower and upper limits; High-pass filter (HPF) pass high

frequency signals and rejects low frequency components; and finally, Band-Reject (Stop) filters that reject signals

with frequencies between a lower and upper limit.

In this laboratory experiment we will plot the frequency response of a network by analyzing RC passive filters (no

active devices are used such as opamps or transistors). We can characterize the filter by two features of the frequency/nresponse:

1. What is the difference between the magnitude of the output and input signals (given by the amplitude ratio)

And

2. What is the time lag or lead between input and output signals (given by the phase shift)

To plot the frequency response, several frequencies are used and the value of the transfer function at these

frequencies is computed. A particularly important method of displaying frequency response data is the Bode plot.

According to your lecture notes, a Bode plot is the representation of the magnitude and phase of H(s) if H(s) is the

transfer function of a system and s = jw where w is the frequency variable in rad/s.

ECEN325 Laboratory Manual, Lab 1

Phase measurement

A method to measure the phase angle by determining the time shift At as shown in Fig. 1, is to display the input and

output sine waves on the two channels of the oscilloscope simultaneously and calculating the phase difference as

follows,

Amplitude

Time shift

Time period

Fig. 1. One way of measuring phase angle.

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Time/nPhase difference =

Where At is the time-shift of the zero crossing of the two signals, and T is the signal's time period.

Pre-laboratory exercise

1. (1.5pt) For the circuit shown in Fig.2, derive the transfer function for vo/vin in terms of R, C, and jw, and

find the expressions for the magnitude and phase responses.

vo

Vin

360.At

T

+jw

wp

Vin(t)

1+1

Where w, is the pole frequency location in radians/second.

R

Vo(t)

Fig.2. First order lowpass filter (integrator)

2. (1pt) The corner frequency of the lowpass filter is defined as the frequency at which the magnitude of the gain

is 0.707 (1/√2) of the DC gain (@= 0). This is also called the half power frequency (since 0.707² = 0.5), and

the -3dB frequency since 20logio(0.707)=-3dB. Find, in terms of R and C, the frequency in both Hz and in

rad/s at which the voltage gain is 0.707 of the DC gain (@= 0).

3.

(1.5pt) For C=10nF, find R so that the -3dB frequency is 4.8 KHz. Draw the bode (magnitude and phase) plots

On the semi-log graph

4.

(2pts) Simulate the low pass filter circuit using the PSpice simulator (Capture CIS 17.4 ). Compare the

simulation results with your hand-calculation. Attach the magnitude and phase simulation results and compare

them to your bode plots from part 3.

2 | Page/nECEN325 Laboratory Manual, Lab 1

5. (2pts) For the circuit shown in Fig. 3, derive the transfer function for vo/vin in terms of R1, R2, C, and jw,

and find the expressions for the magnitude and phase responses. Express your results in the form

Vin(t)

vo

1

Vin (1+Jw)(1+ jwj

jw

wp1' wp2

Lab Measurement:

Part A. First order low pass filter

R1

R2

Vo(t)

Fig. 3. Second order low pass filter

where wp1 and wp2 are the pole frequency locations (in radians/second) in terms of R1, R2, and C.

6. (2pts) Design (find component values) a passive second-order low pass filter such as the one shown in Fig. 3.

Determine R1 and R2 for C=10nF such that the first pole is at 3400 Hz and the second pole is at 34 Hz. You

must use PSpice to verify your design.

1. Build the circuit shown in Fig.2 with the values of R and C you choose in the prelab. Apply a 6Vpp sinusoidal

signal from the function generator to the input, using the high Z option on your signal source (to set the function

generator to High Z: press the output menu button →Load Impedance → High Z then press the L button twice).

2. Connect channel 1 of the oscilloscope across Vin(t), and channel 2 across V.(t). Set the oscilloscope to display

both inputs vs. time by pressing CH1 and CH2. Keep the function generator voltage constant. Vary the

input frequency and find the -3dB frequency (first determine the low frequency, DC gain and then sweep the

frequency until the output is 3dB below the input. Then take a few measurements around this frequency to find

the exact one) take a screen shot. Your data should include several points above and below the -3dB frequency,

if possible, within a couple of decades around that frequency, your data should include the frequency and the

pk-pk measurement of the input as well as the pk-pk measurement of the output.

3. Use the phase measurement on the oscilloscope to measure the phase shift, , between the input and output

signals for at least 10 different frequencies in the range 0.1 f-3dB and 10 f-3dB, including f.38. Measurement of

the phase shift is an accurate method of determining the -3dB frequency. What is the phase shift at f-3dB? Fill

your data in table 1 on the last page.

4. Use the phase measurement way as in Fig 1 to find the phase difference between the input and output signals

at the corner frequency (f-3dB) and compare it with the value you got it in step 3./nPart B. Second order low pass filter

1.

Build the circuit shown in Fig. 3 with R and C you found in the prelab. Apply a 6Vpp sinusoid from the

function generator to the input.

2.

Find the -3dB signal-attenuation frequency f-3dB and 40dB signal-attenuation frequency f-40dB. take screen

shots for both readings. Fill the data in table 2.

Lab Report:

1. Present clearly all your results. Plot the magnitude and phase responses on the semi-log graph (you can use

any tool to plot your data like MATLAB, Python, or Excel); see your lecture notes or textbook for some

examples.

2.

3.

4.

Describe and comment on the differences you found in both first- and second-order low pass filters; consider

both magnitude and phase characteristics.

Compare the hand calculated, PSpice simulated and measured results. Comment on possible reasons for any

differences between them.

Include some conclusions.

ECEN325 Laboratory Manual, Lab 1

Table 1: Data for the first order low pass

Frequency (kHz)

Vin (Vpk-pk)

0.5

1.5

2.5

3.5

4.5

4.6

4.7

4.8

4.9

filter.

V. (V pk-pk)

Gain (V/Vin)

V/V

dB

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Phase shift (p)

degrees/nf3dB

=

4.8

f -40dB =

4.9

5.0

5.1

5.2

5.5

10

15

20

30

Table 2: Data for the second order low pass filter.

Frequency (Hz)

Vin (Vpk-pk)

40

50

100

: Phase difference between input and output wave

Lab instructor signature:

V. (V pk-pk)

Gain (V/Vin)

V/V dB

Phase shift (4)

degrees

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