# #4evaLIVERPOOL- UNITED

To begin with, this lab report done by LO is aimed at Passive Network 1 and 2. Initially passive networks 2 determining the transient response and frequency response of second LRC networks, in addition to how to interpret data in graphical form and to practice soldering. Thus the lab inclined knowledge of being able to identify a second order system as well as being able to calculate frequency response and time response for RLC circuits in addition to being able to test and record data from a second order system.

Initially, though second order circuits exist in different forms, the behavior of LCR circuits and the examination of the resonant behavior. Thus, the word resonance is defined as the key phenomenon in electronic and electrical engineering because it occurs when a resonant circuit is excited or agitated by a frequency to equal and match to its own natural frequency, which in a layman’s words is a frequency to which makes the circuit respond and react to it in a particular marked way. Thus engineers exploit and manipulate these properties of resonance extensively in many ways; communications, signal processing and power management.

The first experiment done, was a series resonant circuit and being more specific, was to build the RLC series circuit shown in the diagram below.

Once this circuit has been setup, the following procedures were followed and the aim was to test the frequency response LR.

Procedure that was followed;

- Set the signal generator to 1 Vrms and to check with the DMM
- Vary the frequency from 1kHZ to 50kHZ
- Connect the oscilloscope to show Vin and Vr
- Take measurements of Vr increasing the frequency
- At the resonant frequency measure Vr, VL, Vc
- How was the resonance and frequency determined

And to later erpeat all the steps using a resistor with 1.2K ohms

Equipment used;

- Two resistors, 100 ohms and 1.2 kilo ohms
- Capacitor
- Inductor
- Oscilloscope

The accuracy of the oscilloscope used during my experiments as referenced from the internet is below

Oscilloscope

Bandwidth specification

Other amplitude accuracy specification

Keysight DSO6054A

*Bandwidth (-3 dB)*

DC-500 MHz

*DC vertical gain accuracy*

±2.0% of full scale

__For 100ohm; table LCR __

Frequency/kHZ

Vr/V

Vin/V

1

0.250

3.275

2

0.432

3.313

5

1

5.103

10

2.85

4.5625

20

2.45

4.4125

50

1.975

4.5255

Frequency/kHZ

Vr/Vin

1

0.076

2

0.115

5

0.1996

10

0.405

20

0.551

50

0.436

Resonance frequency was determined using the gain (Vr/Vin) vs Frequency . Thus the peak of the graph shows where Vr=Vc shows resonance for at this point Vr = V __For 1.2kilo ohms__

Frequency/kHZ

Vx/V

Vin/V

1

0.120

3.34

2

0.169

3.90

5

0.260

4.54

10

0.320

4.70

20

0.960

4.30

50

0.320

4.70

Frequency/kHZ

Vr/Vin

1

0.0359

2

0.0410

5

0.0441

10

0.068

20

0.2230

50

0.0680

Resonance frequency was determined using the gain (Vr/Vin) vs Frequency. Thus the peak of the graph shows resonance

Comparisons of plots – Shape and real vs theoretical

= Shape of the graph is in a ‘Bell Shape’ and it was seen that the peak value gives the resonant frequency. Thus the theoretical value of the resonant frequency is more than the real value of resonant frequency.

The Q factor is called the magnification factor or the quality factor. In a layman’s word is the measure of the magnification of the voltage developed across the L and C at resonance compared with the input voltage. The change in frequency of a circuit is defined as the difference between the frequencies at which the power dissipated is half of the power dissipated at resonance.

Estimation of the value of Q value using the formal f/change in f (where F= frequency) and the plot of experimental results

= Q= f/change in f

Q=0.58/(50k-11k)

Q= 1.51*10-1

Comparison of the Q value to the theoretical value

= Q= 1/R (L/C) exp0.5

Q= 1/100(4.7*10-2/0.01*10-6) exp0.5

Q= 0.1874

Thus the theoretical value is a bit higher than the real value of Q. So it is safe to say that the magnification at the voltage developed across the L & C at resonance compared with input voltage.

**Another experiment; Parallel LRC For 100ohms**

Frequency/kHZ

Vr/V

1

1.37

2

1.33

5

1.13

10

0.720

20

0.200

50

0.265

100

1.29

200

1.64

500

1.93

Thus the peak of the graph shows resonance

Graph of Vr/V vs Frequency

__For 1.2kilo ohms__

Frequency/kHZ

Vr/V

1

2.65

2

2.65

5

2.65

10

2.49

20

1.32

50

2.68

100

2.81

200

2.81

500

2.81

Thus the peak of the graph shows resonance

Graph of Vr/V vs Frequency

Thus my Initial Finding with the Parallel LCR in terms off the comparison of plots and the shape and real vs theoretical.

= The graph was a “U “ shape and the real graph is more steeper than the theoretical graph.

To conclude, referencing an article on google about oscilloscopes and their errors online, an experiment is not 100% accurate due to errors within the instrument and the experimenter thus it was not a 100%.

For, there are many sources of error when operating the oscilloscope such as calibration error and the analysis error. The accuracy of the components used within the oscilloscope and can be assumed to be 5% for both voltages and times.

The final results from the accuracy with which a reading can be made from the screen, and is often related to the line width of the trace. Merging the calibration and analysis errors find the total error of any reading. In most cases the reading error will be considerably smaller than the calibration error.

Comparably the error when setting up a waveform on a signal generator will be due to the adjustment error which is 5% and a setting error thus, the final is related to the scale and width of the cursor.

As the procedure indicates, compare the parameters of a signal produced by a signal generator and that measured by an oscilloscope. In this case both the voltage and frequency which involve errors as set on the signal generator should be compared with the values determined by the oscilloscope.

However, Passive Networks 1 is determining the transient response and frequency response of first order LR and RC networks, in addition to how to interpret data in graphical form and to practice soldering. Thus the lab inclined knowledge of being able to identify a first order system as well as being able to calculate frequency response and time response for LR and RC circuits in addition to being able to test and record data from a second order system.

Thus, Once this circuit has been setup, the following procedures were followed and the aim was to test the frequency response LR. __Procedure that was followed;__

__For the Frequency Response LR__

- Set the Signal Generator to 1V peak
- Vary the frequency from 1kHZ to 500Khz
- Connect the oscilloscope to show Vin and Vout
- Take measurements of Vout increasing the frequency in multiples of 1,2,5&10
- Calculate the log of the frequency
- Calculate the gain (Vout/Vin)
- Plot a log-lin graph of log (frequency) against gain
- Identify the corner frequency
- Calculate the real value of inductance from the corner frequency and compare to that identified by the coloured bands

__ Finding the time constant LR__

- Set the Signal Generator to 5Vpeak, square wave, 10kHz
- Connect the oscilloscope to show Vin and Vout
- Measure the rise time of Vout (from 10% to 90%)
- Set the trigger level 50%, adjust Horiz and Vert scale to display one cycle
- Measure the rise time
- Measure the fall time
- Calculate the time constant
- Calculate the real value of inductance from the corner frequency and compare to that identified by the coloured bands.

__Time constant RC__

- Set the Signal Generator to 5V peak, square wave, 10kHz
- Connect the oscilloscope to show Vin and Vout
- Measure the rise time of Vout (from 10% to 90%)
- Set the trigger level 50%, adjust Horiz and Vert scale to display one cycle
- Measure the rise time
- Measure the fall time
- Calculate the time constant
- Calculate the real value of inductance from the corner frequency and compare to that identified by the coloured bands.

__Frequency Response RC__

- Set the Signal Generator to 1Vpeak
- Vary the frequency from the 1kHZ to 500kHz
- Connect the oscilloscope to show Vin and Vout
- Take measurements of Vout increasing the frequency in multiples of 1,2,5&10
- Calculate the log of the frequency
- Calculate the gain (Vout/Vin)
- Plot a log-lin graph of log (frequency) against gain
- Identify the corner frequency
- Calculate the real value of inductance from the corner frequency and compare to that identified by the coloured bands.

__Data Table RL; Freq vs Vout__

Frequency/kHz

Vout/V

Log(frequency)/kHz

Vout/Vin

1

2

0.0

2

10

2

1.0

2

50

1.8

1.7

1.8

100

1.7

2.0

1.7

200

1.2

2.3

1.2

300

0.8

2.5

0.8

400

0.6

2.6

0.6

500

0.4

2.7

0.4

__Data Table RC; Freq vs Vout__

Frequency/kHz

Vout/V

Log(frequency)/kHz

Vout/Vin

1

20

0.0

20

10

20

1.0

20

50

20

1.7

20

100

18

2.0

18

200

13

2.3

13

300

10

2.5

10

400

10

2.6

10

500

3.6

2.7

3.6

__Initial findings__

LR Corner Frequency; 350 kHZ

LR Measured value of Inductance; 4700 ohms

LR Rise time; 3.0 microseconds

LR Time Constant; 2.4 microseconds

LR Measured Value of Inductance; 4700 ohms

RC Corner Frequency; 96711 Hz

RC Measured value of Capacitance; 2.2nanoFarad

RC Rise; 1.6 microseconds

RC Fall time; 2.8 microseconds

RC Time Constant; 0.79 microseconds

RC Measured Value of Capacitance; 2.2 Nano Farad

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