Picture of Experiment

Practicum 8a working with Bode plot 1

RC-LPF

V1

R1

1kΩ

C11µF V2

Calculations1. Determine the complex transfer function H(ω) = u2/u1

H (ω )=U o

U i

U o=V 2=

1jωC1jωC

+R×U i=

11+ jωCR

×U i

U i=¿ V1

Uo

U i

=

U i

1+ jωCRU i

= 11+ jωCR

C=1μF R = 1000Ω

H (ω )= 1

1+10−3ωj

2. Determine the cut-off frequency of H(ω)

Standard function H (ω )= 1

1+ jωωk

ωωk

=10−3×ωωk=2πf=1000 f=159 rad /s

3. Draw the Bode-plot of H(ω): damping D (in dB’s) and phase

ω=0|H (ω )|=0

ω≫ωk|H (ω )|=−∞

f=159|H (ω )|=−3dB

¿ω=0¿ω≫ωk¿f=159¿

159

Freely Drawn Bode Plot

Real Data :

Simulated and Real Data :

Research questions :

A. Is there a difference between simulation and measurement?There is a very slight difference between the simulated and measurement value .

B. Is it different from the hand drawn Bode plot?No , there is barely any difference between the hand drawn bode plot and the actual plot values , but there is a difference in the shape of the graph but the general shape is correct

Picture of the apparatus :

List of components:1 x NI myDAQ1 x 100 Ω resistor.1 x 1 µF capacitor.1 x LM317 Op Amp

Results from actual experiment :

Research questions

Is there a difference between simulation and measurement?

The two measurements are roughly the same with slight differences such as the peak in the Gain diagram , and the steepness of the line in the phasor diagram .

Is it different from the hand drawn plots ?

The difference is almost negligible between the hand draw plot and the measurement but for the real and the hand drawn plot have the same differences as the simulated and real measurement have as shown above

Is the quality factor equal to the calculated value ?

The values are very close but no equal due the fact that the inductor has a real resistance which was not taken into account in our calculation , and that resistance results in the damping of the quality factor hence resulting in a slightly lower quality factor than the calculated one .

Schematics of the experiment :

List of components:

NI myDAQ

100 mH inductor.

Resistors100 Ω, 162 Ω.

LM317 Op Amp.