# Lab 3 RS

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RC Low-pass filter

# 1-50 kHz filter (20 pnts)

1. Design a low-pass RC filter with a break point between 1-50 kHz. The break point is the frequency at which the filter starts to attenuate the AC signal. For a Low pass filter, AC signals with a frequency above 1-50 kHz will start to be attenuated (not passed)

To design low-pass RC filter I had:




So





2. Now construct the circuit using a non-polar capacitor

3. Use a sinusoidal variable frequency oscillator to provide an input voltage to your filter

4. Measure the input and output voltages for at least 8 different frequencies which span the frequency range from 1 Hz to 1 MHz

Table1. Voltage gain vs. frequency measurements
0.1 5.0 5.0 1.0
1.0 4.2 4.2 1.0
2.0 3.2 3.1 0.97
5.0 1.8 1.6 0.89
10.0 1.14 0.88 0.77
16.7 0.90 0.54 0.60
20.0 0.88 0.48 0.54
25.0 0.82 0.38 0.46
33.3 0.78 0.28 0.36
50.0 0.76 0.18 0.24
100.0 0.75 0.09 0.12
125.0 0.74 0.07 0.095
200.0 0.75 0.04 0.053
333.3 0.76 0.03 0.039
200.0 0.76 0.03 0.039
1000.0 0.78 0.06 0.077

5. Graph the -vs-

# phase shift (10 pnts)

1. measure the phase shift between and as a function of frequency . Hint: you could use as an external trigger and measure the time until reaches a max on the scope .
See question 4 about my phase shift measurements


# Questions

## 1. Compare the theoretical and experimentally measured break frequencies. (5 pnts)

### method 1. Using fitting line

Theoretical break frequency:

The fit line equation from the plot above is . From intersection point of line with x-axis we find:

The error is:




### method 2. Using the -3 dB point

At the break point the voltage gain is down by 3 dB relative to the gain of unity at zero frequency. So the value of . Using this value I found from plot above . So . The error in this case is

## 2. Calculate and expression for as a function of , , and . The Gain is defined as the ratio of to .(5 pnts)

We have:

Dividing second equation into first one we get the voltage gain:

And we are need the real part:

## 4. Compare the theoretical and experimental value for the phase shift . (5 pnts)

The experimental phase shift is

The theoretical phase shift is


## 5. What is the phase shift for a DC input and a very-high frequency input?(5 pnts)

Because a DC circuit doesn't have any oscillation there are no any phase shift.

For a very high frequency input the phase shift is -90 degree (see plot in question 6)


## 6. Calculate and expression for the phase shift as a function of , , and graph -vs . (20 pnts)

From the phasor diagram above (question 3) the angle between vectors and given by