EE 420L Engineering Electronics II - Lab 1

Eric Monahan

monahan@unlv.nevada.edu

2/3/16

 

Lab 1: Review of Basic RC Circuits

For this first lab simulate, and verify the simulation results with experimental measurements, the circuits seen in Figs. 1.21, 1.22, and 1.24 (use a 1 uF cap in place of the 1 pF cap) of the book. Your results should be similar to, but more complete than, the simulation results seen on pages 17 - 23.  In your report, and for each circuit, show the



Experiment 1: Circuit Fig 1.21

The circuit in Figure 1.21 below is an RC circuit with a 1V input at 200Hz connected to a 1kΩ resistor in series with a 1µF capacitor. This circuit and the two circuits following this experiment were all simulated in LT Spice to obtain simulated values to be compared to hand calculated theoretical values and experimental values obtained in the laboratory. A table showing a comparison of all values will be included below.

 

Circuit Fig. 1.21

 

 

The quantities to be measured in this experiment will be the transfer function, phase response and time delay. Theoretical values obtained via hand calculations are shown in the image below. 

 

Theoretical Values

 

 

The waveform below from the LT Spice simulation displays a transfer function magnitude of approximately 622.5mV and a time delay of approximately 717µs. 

 

Simulation Values

 
Fig 1.21  Transient Analysis                                                                   

An AC analysis was performed to obtain the phase response. The circuit and resulting waveform are shown below. The simulation resulted in a phase response of approximately -51.4. Included below these images is another method of obtaining similar information as obtained in the transient analysis and the AC analysis. This is done to demonstrate the versatility of LT Spice as an analytical tool.

 

     

Fig 1.21 AC Analysis Method 1

 

Fig 1.21 AC Analysis Method 2

 

Comparing the theoretical values to the simulated values above reveals close approximations between the two different methods of analysis.

 

Experimental values are shown below in the oscilloscope images captured during the experiment. The phase response will be calculated using the time delay equation found in the theoretical values and solving for degrees.

The figure on the left  displays an amplitude of 600mV. The figure on the right displays a time delay,  of 800µs. The calculated phase response was -57.6. These values fall within the range of the simulated and theoretical values.

 

Experimental Values

 

         

Fig. 1.21 Amplitude                                                                   Fig. 1.21 Time Delay

 

The table below shows a comparison of the experimental, theoretical and simulation values.

           

Fig 1.21

| (V)

 (

(s)

 

 

 

 

Simulation

0.6224

-51.49

717.3µ

Theoretical

0.6227

-51.49

715.1µ

Experimental

0.6000

-57.60

800.0µ

 

 

The circuit in Fig. 1.21 was used to generate a table showing representative values for the magnitude and phase response. These values were obtained via experimentation and simulation with the results given in the table and plots below. The frequency at 159Hz represents the cut-off frequency.  The plot verifies the decrease in magnitude that occurs once the frequency exceeds the cut-off frequency. This data indicates the circuit acts as a low pass filter, accepting only frequencies below 159Hz and rejecting frequencies above 159Hz.

 

Frequency (Hz)

Experimental Magnitude(dB)

Experimental Phase ()

SImulation Magnitude (dB)

Simulation Phase ()

 

 

 

 

 

1

0.00

0.00

0.00

0.00

10

0.00

-4.20

0.00

-3.61

100

-1.41

-32.4

-1.44

-32.1

159

-2.85

-46.37

-3.04

-45.1

200

-4.21

-54.7

-4.13

-51.6

1k

-14.3

-79.2

-16.1

-80.9

10k

-31.1

-86.4

-36.0

-89.1

100k

-48.3

-89.9

-56.0

 

 

 

 

 

Experiment 2: Circuit Fig 1.22

 

The circuit in Figure 1.22 is similar to the RC circuit in Fig. 1.21 with the addition of a 2µF capacitor in parallel with the 1kΩ resistor. Theoretically, the capacitor in parallel with the resistor should reduce the amount of loss in the strength of the signal when compared to the circuit in experiment one. The same process will be used as in experiment one to compare values and analyze results.  The comparison of values will be included in a table following the images containing the relevant quantities measured during each different type of analysis. 

 

 

Circuit Fig. 1.22

 

 

 

Theoretical Values

 

 

Simulation Values

 

Fig. 1.22 Transient Analysis

 

 

Fig. 1.22 AC Analysis

 

Experimental Values

  

 

Note the similarities between the waveform outputs in the simulation versus the oscilloscope. The values are in the range expected when compared to hand calculations. The table below displays a comparison of measured values. Variances are likely due to occur between the different methods of analysis due to differences in the techniques themselves. For example, the oscilloscope values may differ from the simulation values due to the difficulty in aligning the cursors on the oscilloscope precisely enough to gather accurate data. 

 

Fig 1.21

| (V)

 (

(s)

Simulation

0.6952

-6.854

76.40µ

Theoretical

0.6935

-6.841

95.01µ

Experimental

0.7200

-5.760

80.00µ

 

As seen in the table above, the capacitor in parallel with the resistor served to lower the impedance and reduce the loss in signal strength compared to the circuit in experiment one. The experimental magnitude of the transfer function in circuit one was approximately 600mV versus approximately 720mV for the circuit in experiment two. There was also a noticeable reduction in the time delay and the phase response for experiment two.

 

Experiment 3: Circuit Fig 1.24

 

The circuit in Fig. 1.24 is the same as the circuit in experiment one, but for experiment three the input has been changed to a pulse. Using the pulse will allow calculation of the delay time and the rise time of the signal. The results of the analysis are displayed in the images below. The measured values will be displayed in a table below.

 

Circuit Fig 1.24

 

 

 

Theoretical Values 

 

 

Fig. 1.24 Delay Time                                                                                                                                Fig. 1.24 Rise Time

 

Experimental Values

  

In the above oscilloscope capture, the time delay was captured at 50% of peak output at approximately 760 µs as shown in the image on the left. The rise time was captured between 10% and 90% peak output at approximately 2.36ms as shown in the image on the right. These values fall within the simulation and theoretical values previously obtained.

 

 

The table below displays the values measured in experiment three. The measured values all fall within close range of each other.

Fig 1.21

Simulation

703µ

2.09m

Theoretical

700 µ

2.20m

Experimental

760 µ

                         2.36m

 

 

Conclusion

 

The experiments performed in Laboratory One offered the opportunity to review basic RC circuits, to practice LT Spice simulations and to compare the values obtained via different methods of analysis, specifically experimentation, hand calculation and simulation. The laboratory results also demonstrated the variances that may occur within the different methods of analysis due to different means of measuring inherent in each technique. 

 

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