How to design Circuitry for general Function generation in signal Analysis? Can we use 5 timer for this if yes how?

Objectives:  

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

design and analysis in the frequency domain.  

List of Equipment required: 

a. Protoboard 

b. Capacitors 

c. Resistors 

d. Oscilloscope  

e. Function generator 

f. Frequency counter 

g. Digital Multimeter 

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 

(σ+j). 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; Bandpass 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 limits. 

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 response: 

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, a number of 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 =σ+ j where  is the frequency variable in rad/s.  

Phase measurement

A method to measure the phase angle by determining the time shift t, is to display the input and output sine waves 

on the two channels of the oscilloscope simultaneously and calculating the phase difference as follows,4 -     - 

Fig.1. One way of measuring phase angle. 

Phase difference (in degrees) =

T

t

where t is the time-shift of the zero crossing of the two signals, and T is the signal’s time period. 

Pre-laboratory exercise  

1. For the circuit shown in Fig.2, derive the transfer function for vo/vin in terms of R, and C,  and find the 

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

p

in

o

v s

v







1

1

where ωp is the pole frequency location in radians/second. 

Vo(t)

R

Vin(t) C

Fig.2. First order lowpass filter (integrator)

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

is   0. of the DC gain (ω =0).  This is also called the half power frequency (since0.

2

 =0.5), 

and the -3dB frequency sincelog(0.) = -3dB.  Find, in terms of R and C, the frequency in both Hz 

and in rad/s at which the voltage gain is0. of the DC gain (ω =0). 

3. For C =nF, find R so that the –3dB frequency is3.3kHz. Draw the bode (magnitude and phase) plots. 

4. Simulate the low pass filter circuit using the PSpice simulator. Compare the simulation results with your 

hand-calculation. Attach the magnitude and phase simulation results, and compare them to your bode plots 

from step3.  

5. For the circuit shown in Fig.3, derive the transfer function for vo/vin in terms of Ri

 , and Ci

, and find the 

expressions for the magnitude and phase responses. You may assume R2 >>2R1 

 Express your results in .

the form5 -     - 































1

p p

in

o

s s

v

v

 

where ωp1 and ωp2 are the pole frequency locations (in radians/second)  in terms of Ri

and C.  

6. 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 =nF such that the first pole is at1, Hz and the second pole is at Hz.  

You must use PSpice to verify your design.  

7. Draw the bode plots, and compare them to the magnitude and phase simulation results using PSpice.  

Vo(t)

R1

C C

R2

Vin(t)

Fig.3. Second order low pass filter 

Lab Measurement: 

Part A. First order low pass filter 

1. Build the circuit shown in Fig.2 with the values of  R and  C you choose in the pre lab. Apply a6Vpp 

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

(ask you TA for assistance).  

2. Connect channel1 of the oscilloscope across  vin(t), and channel2 across  vo(t). Set the oscilloscope to 

display both inputs vs. time by pressing CH1 and CH2. Keep the 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 is3dB below the input. Then take a few measurements around this frequency 

to find the exact one). Your data should include several points above and below the –3dB frequency, if 

possible within a couple of decades around that frequency.  

3. Use the cursors on the oscilloscope to measure the time shift, t, between the zero crossings of the input 

and output signals for at least different frequencies in the range0.1f-3dB andf-3dB, including f-3dB, and 

get the phase shifts between input and output signals. Measurement of the phase shift is an accurate method 

of determining the –3dB frequency. What is the phase shift at f-3dB? 

Part B. Noise Filtering

1. Noise filtering is studied in this part. Noise is modeled as a high frequency, small amplitude signal and 

superimposed onto an ideal sine wave. A low pass filter can attenuate the high frequency noise while 

preserving the wanted signal. 

2. Evoke the ArbWave software; 

3. Generate a sine wave. Select a sine wave using the Waveforms icon; 

4. Add noise to signal. Select the edit icon and use the select all utility, then select the math icon, choose the 

add utility. In the add function box, select the standard wave option. Next select the noise waveform and 

adjust it to0.3V. In the add function box, choose the fit amplitude option;  

5. Send the noisy waveform to the signal generator. Use  I/O icon and select  send waveform. Adjust the 

amplitude of the signal to6Vpp, and the frequency to0.kHz; 

6. Apply this signal to your lowpass filter and observe the input and output signals;  

7. Take a screen shot of both the noisy and filtered signals on the oscilloscope