6 Frequency M ultiplying C ircuit ECE 300 Lab 6 Frequency Multiplying Circuit In this lab we look at extracting a higher frequency sine wave from lower frequency square wave 6 A Theory of Operation From our study of the Fourier series expansion of a periodic signal we know that a square wave at frequency Fo is composed of a sum of sinusoidal waves at frequencies nFo where n ranges from 1 to infinity If we take this signal and pass it through a band pass filter that has a pass band narrow enough to filter out all harmonics except one we can obtain a sine wave that has a higher frequency than the fundamental frequency of the square wave For this lab we will use a 2 kHz square wave with an amplitude of 0 5 volts This square wave contains sinusoidal frequencies of 2 kHz 4kHz 6kHz 8KHz 10kHz and higher We will use a 6th order filter with a pass band of 9 kHz to 11 kHz Thus when we pass our 2 kHz square wave through this filter we should obtain a 10 kHz sine wave at the output 6 B Pre Lab Calculations Compute the Fourier series coefficients of a 0 5 volt amplitude square wave Specifically find the magnitude of the 5th harmonic the one at 10 kHz Simulate the circuit of Figure 6 1 You should run two simulations o An AC sweep from 5 kHz to 15 kHz Obtain Bode plots of Vo2 Vin Vo1 Vin and Vo Vin For this simulation use the part VAC for the input voltage source o A Transient analysis to view Vo t For the input use the part called Vsq Set the frequency to 2 kHz and the amplitude to 0 5 Volts Set up the Transient analysis to run for 100 ms and set the maximum time step to 1 s Plot Vo t from 99 ms to 100 ms Use the cursors to measure the amplitude and frequency of this waveform Compare the amplitude of this waveform to the amplitude predicted by the Fourier series expansion An example output waveform is shown in Figure 6 2 Vo Vo2 C1 Vin Vo1 R1 C2 27k C4 U1 R5 V4 C6 7 5k 0 01U U3 0 01U 7 5k R7 Ideal OPAMP R8 0 Ideal OPAMP R9 47 100 0 56k R6 U2 0 01U R3 0 01U C5 12k C3 47k 0 01U 0 01U R4 R2 0 0 FREQUENCY 2k AMPLITUDE 0 5 Figure 6 1 6th order band pass filter 6 1 Ideal OPAMP 56 0 0 0 200mV 100mV 0V 100mV 200mV 99 0ms 99 1ms V Vo 99 2ms 99 3ms 99 4ms 99 5ms 99 6ms 99 7ms 99 8ms 99 9ms 100 0ms Time Figure 6 2 Sinusoidal output of the filter Note A 6th order filter may be very difficult to build and operate If you want you can use the 4th order filter shown Figure 6 6 in instead of the 6th order filter Note that in theory the 4th order filter will not work as well as a 6th order filter in extracting the 5th harmonic However a 4th order filter may be easier to build in the lab 6 C Laboratory Procedure 6 C 2 Building up the Circuit 1 For a large circuit like this it is important to build it in small pieces and verify the operation of each piece Wire up the first stage as shown in Figure 6 3 using a TL072 OP AMP or whatever OPAMP you can find The input should be a 1 volt sine wave or smaller 6 2 Vo2 R1 C1 Vin 27k 0 01U R4 U1 C4 0 01U 12k R7 Vin TL072 100 0 0 0 Figure 6 3 First stage of the band pass filter Using VEE measure a bode plot of Vo2 Vin and compare it to the one predicted by PSpice If the plots agree you can continue with the second stage If the output of this stage is incorrect find the problem before continuing Measurement Results Create a graph that displays the measured and PSpice plots of Vo2 Vin Plot both traces on the same graph 2 Wire up the second stage as shown in Figure 6 4 The input should be a 1 volt sine wave or smaller Vo2 Vo1 27k 0 01U C5 0 01U R8 TL072 100 0 U2 7 5k R7 Vin 0 R5 12k U1 C4 R4 47k 0 01U 0 01U R2 C2 Vin R1 C1 Ideal OPAMP 47 0 0 0 Figure 6 4 First two stages of the band pass filter Using VEE measure a bode plot of Vo1 Vin and compare it to the one predicted by PSpice If the plots agree you can continue with the third stage If the output of this stage is incorrect find the problem before continuing Measurement Results Create a graph that displays the measured and PSpice plots of Vo1 Vin Plot both traces on the same graph 3 Wire up the third stage as shown in Figure 6 5 The input should be a 1 volt sine wave or smaller 6 3 Vo Vo2 Vo1 0 01U 0 0 01U Ideal OPAMP R8 100 7 5k TL072 R7 Vin 7 5k 0 Ideal OPAMP R9 47 0 U3 C6 0 01U R6 U2 C5 R5 56k 0 01U U1 0 01U C4 12k 47k R3 C3 R4 R2 C2 27k 0 01U R1 C1 Vin 56 0 0 0 0 Figure 6 5 6th order band pass filter Using VEE measure a bode plot of Vo Vin and compare it to the one predicted by PSpice If the output of this stage is incorrect find the problem before continuing Measurement Results Create a graph that displays the measured and PSpice plots of Vo Vin Plot both traces on the same graph 6 C 2 Frequency Multiplication Now that the filter is correctly wired we can test it with a square wave input Apply a 0 5 V amplitude 2 kHz square wave to your filter and measure the amplitude and frequency of the output using an oscilloscope Compare the measured amplitude and frequency to the values found from PSpice and the Fourier series expansion Record the results in a table for easy comparison Demonstrate your circuit to your lab instructor Display the input square wave and the output sine wave on the scope display Vo1 Vo 20k C4 U1 R5 C5 R4 0 01U 6 8k R7 6 8k V1 R8 Ideal OPAMP 100 0 U2 0 01U 24k 0 01U 0 01U R2 C2 Vin R1 C1 0 Ideal OPAMP 130 0 0 FREQUENCY 2k AMPLITUDE 0 5 Figure 6 6 4th order band pass filter with a pass band of 9 kHz to 11 kHz 6 4 0
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