Mobile Studio Activity 8 Report

8/9/2019 Mobile Studio Activity 8 Report

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Mobile Studio Activity #8 Adam Steinberger Electric Circuits Section 2

Page 1

Introduction

Transfer functions are particularly useful for alternating current first- and second-order circuitanalysis because they provide the relationship between the input and output of a system in terms of

frequency. Bode Diagrams are used to graphically represent the gain of a circuit (in decibels) as a

function of frequency. Both tools are often used to inspect and/or calculate whether a system acts as a

high-pass or low-pass filter.

ProcedureThe protoboard configuration for this lab is shown in the

image to the right. Green and orange wires were connected on both

sides of each device of the RLC circuit (one at a time), and

measurements were taken using the Bode Analyzer tool from the

LabVIEW Launcher software designed for use with Mobile Studio

cards. Data was then imported into Microsoft Excel and plotted.

Another protoboard used for this lab was configured as is

illustrated in the image to the left. Readings from the Mobile Studio

Desktop software were taken while the potentiometers were both

adjusted so that the peak to peak voltage across the circuit inputs

was no greater than 5mV. Then a multimeter was used to obtain the

resistances of both potentiometers.

AnalysisA transfer function for a port is the ratio of the output voltage divided by the input voltage. By

converting a circuit to its s-Domain impedances, transfer functions for a series RLC circuit can be

evaluated using these impedances instead. For second-order circuits like the one used in this lab,

transfer functions in the s-Domain follow the form

. Bode Diagrams are obtained byconverting these expressions into their decibel equivalents. Cutoff frequencies are found where the gain

is . The distance between the cutoff frequencies is defined as bandwidth, and is equal to .Second-order circuits will respond at their natural resonant frequency, which can be calculated byevaluating the impedance of the circuit as a function of . Analytical proof shows that thisfrequency is .

Mathematical analysis of circuits like the second one used in this lab illustrate that inductance

can be measured indirectly as a function of certain resistances within the circuit. The evaluation for this

special circuit resulted in an inductance with an error of only 2mH. The resistance of the inductor was

also calculated, and the result was only off by 1.


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Page 2

ConclusionTransfer functions and Bode Diagrams are invaluable tools used by Electrical Engineers for AC

transient circuit analysis. Using transfer functions, circuits can be treated as systems of ports where each

port has a specific input/output relationship. The results from this kind of analysis can then be plottedon Bode Diagrams as frequency responses, which allow engineers to inspect the circuits for high- and

low-pass filtering.


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Page 3

Data

Transfer Function for Resistor

() ()()

()

() ()()

|

|

()

Transfer Function for Capacitor

() ()()

()

() ()()

|

|

0

V1

FREQ = {F}VAMPL = 0.5VOFF = 0

R1

500

L1

1mH

1 2

C1

10u

PARAMETERS:

F = 1k


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Page 4

()

Transfer Function for Inductor and Capacitor

() ()()

()

()

()()

()

Resonant Frequency() () () ( )


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Page 5

LX and RX of Unknown Inductor

()

R2

10k

R3

1k

V2

FREQ = 1kVAMPL = 0.5VOFF = 0

C222u

R41k

R_coil

?

L_coil

?

1

2

A1+ A1-


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Page 6

Figure 1 - LabVIEW: Bode Gain Analysis for Resistor

Figure 2 - LabVIEW: Bode Phase Analysis for Resistor

-14

-12

-10

-8

-6

-4

-2

0

2

10 100 1000 10000 100000

Gain

(dB)

Frequency (Hz)

Bode Gain Analysis for Resistor

-80

-60

-40

-20

0

20

40

60

80

100

10 100 1000 10000 100000

Phase

(deg)

Frequency (Hz)

Bode Phase Analysis for Resistor


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Page 7

Figure 3 - LabVIEW: Bode Gain Analysis for Inductor

Figure 4 - LabVIEW: Bode Phase Analysis for Inductor

-60

-50

-40

-30

-20

-10

0

10 100 1000 10000 100000

Gain

(dB)

Frequency (Hz)

Bode Gain Analysis for Inductor

-20

0

20

40

60

80

100

120

10 100 1000 10000 100000

Phase

(deg)

Frequency (Hz)

Bode Phase Analysis for Inductor


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Page 8

Figure 5 - LabVIEW: Bode Gain Analysis for Capacitor

Figure 6 - LabVIEW: Bode Phase Analysis for Capacitor

-70

-60

-50

-40

-30

-20

-10

0

10

10 100 1000 10000 100000

Gain

(dB)

Frequency (Hz)

Bode Gain Analysis for Capacitor

-120

-100

-80

-60

-40

-20

0

20

10 100 1000 10000 100000

Phase

(deg)

Frequency (Hz)

Bode Phase Analysis for Capacitor


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Page 9

Figure 7 - LabVIEW: Bode Gain Analysis for Inductor and Capacitor

Figure 8 - LabVIEW: Bode Phase Analysis for Inductor and Capacitor

-45

-40

-35

-30

-25

-20

-15

-10

-5

0

5

10 100 1000 10000 100000

Gain

(dB)

Frequency (Hz)

Bode Gain Analysis for Inductor and Capacitor

-120

-100

-80

-60

-40

-20

0

20

40

60

80

100

10 100 1000 10000 100000

Phase

(deg)

Frequency (Hz)

Bode Phase Analysis for Inductor and Capacitor


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Page 10

Figure 9 - PSPICE Simulation: Bode Analysis for Resistor

Figure 10 - PSPICE Simulation: Bode Analysis for Inductor

Frequency10Hz 30Hz 100Hz 300Hz 1.0KHz .0KHz 10KHz 30KHz 100KHz

V(L1:1,C1:2)0V

50mV

100mV

150mV

200mV

250mV

300mV

350mV

400mV

Frequency

10Hz 30Hz 100Hz 300Hz 1.0KHz .0KHz 10KHz 30KHz 100KHzV(R1:1,L1:1)

100mV

150mV

200mV

250mV

300mV

350mV

400mV

450mV

500mV


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Page 11

Figure 11 - PSPICE Simulation: Bode Analysis for Capacitor

Figure 12 - PSPICE Simulation: Bode Analysis for Inductor and Capacitor

Frequency10Hz 30Hz 100Hz 300Hz 1.0KHz 3.0KHz 10KHz 30KHz 100KHz

V(L1:1,0)0V

100mV

200mV

300mV

400mV

500mV

Frequency

10Hz 30Hz 100Hz 300Hz 1.0KHz 3.0KHz 10KHz 30KHz 100KHzV(C1:2,0)

0V

100mV

200mV

300mV

400mV

500mV


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Page 12

Figure 13 - MATLAB Plot: Bode Gain Analysis for Resistor

Figure 14 - MATLAB Plot: Bode Gain Analysis for Capacitor


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Page 13

Figure 15 - MATLAB Plot: Bode Gain Analysis for Inductor and Capacitor

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