Essays on Bode Plot

1. The bode plot of the system is:

The zeros are located at:

f=0, 500 Hz

The poles are located at:

f=3.4, 50, 2120 Hz 2. Converting Hz to rad/s,

Zeros:

ωz1=0, ωz2=2π500=1000π

Poles:

ωp1=2π3.4=21.36, ωp2=2π50=100π, ωp3=2π2120=4240π 3. The form of the transfer function is: Hs=Kss+1000π(s+21.36)(s+100π)(s+4240π) Hs=j2.136=1=Kj2.136j2.136+1000π(j2.136+21.36)(j2.136+100π)(j2.136+4240π) 1K=7.47×10-5→K=13387

The transfer function becomes:

Hs=13387ss+1000πs+21.36s+100πs+4240π =13387ss1000π+11000πs21.36+1s100π+1s4240π+121.36100π4240π H(s)=0.4705ss1000π+1s21.36+1s100π+1s4240π+1 4. The frequency response of the transfer function is generated in MATLAB using the following code: clc s = tf('s'); wz = [1000* ...

PURPOSE

Design an active second order Low-pass filter and characterize its frequency response.EQUIPMENT AND COMPONENTS Oscilloscope Power Supply Function Generator UA741 or LM741 OP AMP 4.7 nF Capacitors

Resistors

PRELAB 1. The RC circuit is shown in the following figure. Node Voltage Analysis is done in order to generate a transfer function Tvs=V2sV1s. In the circuit, voltage at node A is also the input voltage (V1=VA), and voltage at node D is also the output voltage (V2=VD).

KCL at node B:

V1-VBR1=VB-V21/sC1+VB-VCR2 (1)

KCL at node C:

VB-VCR2=VC1/sC2 (2) V2=uVC→VC=V2u (3)

Simplifying (2):

VB=VC1+sR2C2 (4)

Then, substituting (3) to (4):

VB=V2u1+sR2C2 (5)

Substituting (3) and (5) to (1):

V1-V2u1+sR2C2R1=V2u1+sR2C2-V21sC1+V2u1+sR2C2-V2uR2 V1-V2u1+sR2C2R1=V2u1-u+sR2C21sC1+V2usR2C2R2 V1-V2u1+ ...

Objective:

This experiment is about the implementation and testing of low-pass, high-pass, and band-pass filters. The frequency response of each filter is analyzed using Bode plots. The properties of passive devices will be used to explain the response.

Equipment List:

EQUIPMENT Oscilloscope 2 Function Generators

COMPONENTS

1µF Capacitors 1 kΩ Resistors

Relevant Theory/Background Information:

A low-pass filter is a filter that allows frequencies below a cut-off frequency while filtering out frequencies above this cut-off frequency. For a simple series RC circuit, a low-pass filter can be created by connecting the input signal to the resistor and taking the output from the capacitor. The cut-off frequency ...