report
Abstract
The objective of this design project is to construct and demonstrate an AM radio which capable of modulating, and transmitting over wireless. The AM radio also capable of demodulating single tone AM-modulated signal (we call this signal s(t)), this single tone can be any frequency between 200Hz and 4KHz.BNC cable would be use to connect between transmitter and receiver. Signal m(t) (demodulated single tone sine wave) should be displayed without distortion on the digital oscilloscope and should be clearly audible when play on a speaker. Input can be from the function generator sine wave or from a microphone.
In this report,we will go over the theoretical part of the design project. Each component would be build simulate individually then combine with previous component and simulate, in other word this report will go over the transmitter theoretical part step by step. We were able to meet all the requirements (more on how each component meet the requirement as we go in the theory section).
Introduction
There are two parts of this design project, this interim report only cover the AM transmitter theoretical part.
There are some specifications required for the transmitter components:
Carrier frequency f_c of the carrier wave c(t) must be between 40KHz-60KHz.
Transmitter band pass filter frequency response |H(f)| specifications:
Lower stop band: 20?log?_10 (|H(f)|) = -20 dB for f = 4 kHz.
Upper stop band: 20?log?_10 (|H(f)|) = -10 dB for f = 2f_c.
Pass band: -2 dB = 20?log?_10 (|H(f)|) = 2 dB for f_c–4000 = f = f_c+4000Hz
The receiver’s antenna should pick up the signal at least 12 inches away from the transmitting antenna.
Figure 1 shown a block diagram of the AM transmitter. Each block represents a component, for this section we will touch briefly on each component.
Signal generator (or microphone): This component could be a microphone or a sine wave signal from function generator, this signal is the tone frequency (or the data) we will transmit.
Oscillator: This component will generate a wide range of frequency.
Switching Modulator: This component will multiply the signal generator and the signal from the oscillator.
Band Pass Filter: This component filter out a certain bandwidth (certain range of frequency).
Power Amplifier: This component amplifier the signal from the band pass filter.
Antenna: This component transmits the amplified signal.
The purpose of this interim report is to go over the theoretical part of the AM transmitter step by step. By design each component and simulate them give us a better understanding of the whole project.
Figure 1. Block Diagram of the AM transmitter
Theory
Signal Generator
Figure 2 shown a signal generator, m(t) this is the data that need to transmit, this signal can be either come from the function generator or microphone. Sound is produced when air vibrate, hence certain frequency has different sound. If we sweep the function generator (that is to change the frequency output of the function generator), the sound produced by the speaker should be different.
Figure 2. Signal Generator, m(t)
Wien Oscillator
Figure 3 shown the circuit of Wien Oscillator. The Wien Oscillator is responsible to generate the carrier frequency, f_c. The design requirement for carrier frequency is 40KHz<f_c<60KHz. The reading material provide steps to estimate ideal values forC,R and R_1,R_2. The loop gain can be obtained by multiplying the transfer function H(s) with the amplifier gain:
L(s)=[1+R_2/R_1 ] Z_p/(Z_p+Z_s ) (1)
Where Z_p is the equivalent impedance of R an C in parallel, and Z_s is the equivalent impedance of R an C in series. Replace the equivalent impedance we have:
L(s)=(1+R_2/R_1 )/(3+sRC+1/sRC) (2)
Substituting s=j? to equation (2)
L(s)=(1+R_2/R_1 )/(3+j?RC+1/j?RC) (3)
The loop gain will be a real number, meaning that the phase will be zero at a certain frequency given by:
?_0=1/RC (4)
The magnitude of the loop gain to unity should be able to sustained oscillator at this frequency, which is given:
R_2/R_1 =2 (5)
However, we chose R_2/R_1 =7 that is R_2=7K? and R_1=1K?. Now choose a value for C, the reason chose C before R is because there is only so much value C can be, R on the other hand can be more flexible. We chose C=1nF and instead of calculating R, we chose to do a trial and error. Changing value of R would affect the carrier frequency which is 40KHz<f_c<60KHz, any f_c in that range would be fine. We came up with R=650?, simulate the circuit give us the carrier frequency f_c=51.85KHz. To simulate the circuit and find the carrier frequency, we used the build in function of PSPICE called Fast Fourier Transform. This function converts a signal from time domain to frequency domain. Figure 4 shown the Wein Oscillator output signal. Figure 5 shown the Wein Oscillator output after using Fast Fourier Transform. Figure 6 shown carrier frequency obtained by zoom into the maximum overshoot of the Wein Oscillator output after using Fast Fourier Transform. We met the design requirement #5.
Figure 3. Wien Oscillator circuit
Figure 4. Wein Oscillator output signal
Figure 5. Wein Oscillator output after using Fast Fourier Transform
Figure 6. Carrier Frequency
Switching Modulation
This module multiply two signals (signal from signal generator, m(t) and signal from the Wein Oscillator, c(t)), and filter out the negative envelope (this done by using a diode).The diode is there to multiply, modulate the signal from the summer circuit (m(t)+c(t)). Figure 7 shown a simple representation of the module.
Figure 7. Simple representation of Switching Modulation
From figure 7, D is an ideal diode, c(t) is signal from Wien Oscillator, m(t) is data signal (from signal generator). The switching modulation will multiply c(t) and m(t), where: c(t)=A_c cos?[(2pf_c )t] then the signal come out of the switching modulation is s(t)=c(t)[1+k*m(t) ]=A_c [1+k*m(t) ]cos?[(2pf_c )t] . Where k is a constant, A_c is the amplitude of the carrier wave, and f_c is the carrier frequency.
Figure 8 shown the circuit of switching modulation. As you can see there are two difference waves with difference frequency. Simulate this circuit give us figure 9, there are two waves in figure 9, m(t) the message wave which is 2Hz and c(t) the carrier wave which is 200Hz. Figure 10 shown a zoom in on figure 9 to see the carrier wave better.
Figure 8. Switching Modulation
Figure 9. Switching Modulation simulation
Figure 10. Zoom in on figure 9
The modulation work as expect, it block the negative half of the envelope, the magnitude seem correct R_2/R×(V_1+V_2 )-V_D=2×(1)-0.6V=1.4V. Now hook the signal generation, m(t) and the carrier signal c(t) to the switching modulation, then simulate it. Figure 11 shown a complete circuit, figure 12 shown the simulation result of m(t) with 200Hz input, and figure 13 shown the simulation result of m(t) with 4KHz input.
Figure 11. Completed Circuit thus far
Figure 12. Switching Modulation 200Hz
Figure 13. Switching Modulation 4KHz
Doing a quick assessment of figure 12 and figure 13, we can tell that at both frequency the output has the same amplitude, and the 4KHz has way shorter wave length compare to 200Hz. Also, because 4KHz has shorter wave length we can see that the carrier frequency fill the whole thing less compare to 200Hz. In other word, there are 52000/4000=13peaksin a wave length (for 4000Hz), compare to 52000/200=260 peaks in a wave length (for 200Hz). This explain why 200Hz looks more fill than 4000Hz.
Band Pass Filter
This module is used to filter unwanted frequency and pass a certain band frequency. The main goal is to use two Butterworth active filters to pass the carrier frequency (52KHz±4KHz) and filter unwanted frequencies. The band pass filter made up by two Butterworth filters: Butterworth high pass filter (filter out everything lower than 52KHz-4KHz=48KHz, in other word has the cutoff frequency of 48KHz), and Butterworth low pass filter(filter out everything higher than 52KHz+4KHz=48KHz, in other word has the cutoff frequency of 56KHz).
Figure 14 shown a circuit of Butterworth active high pass filter which has the cutoff frequency of 48KHz. Simulate the circuit by sweeping the frequency, the dB plot (or Bode plot) can be obtained, figure 15 shown this plot. The design requirement is met, lower stop band magnitude20?log?_10 (|H(f)|) = -20 dB atf = 4 kHz, see figure 16.
Figure 14. Butterworth active high pass filter
Figure 15. High pass filter Bode plot
Figure 16. Lower band magnitude requirement
Figure 17 shown a circuit of Butterworth active low pass filter which has the cutoff frequency of 52KHz. Simulate the circuit by sweeping the frequency, the dB plot (or Bode plot) can be obtained, figure 18 shown this plot. The design requirement is met, higher stop band magnitude20?log?_10 (|H(f)|) = -10 dB forf = 2f_c, see figure 19.
Figure 17. Butterworth active low pass filter
Figure 18.Low pass filter Bode plot
Figure 17. Higher band magnitude requirement
A band pass filter can be built by putting the high pass and low pass filter together. The band pass filter would pass frequencies from f_1=48KHz (the cutoff frequency of high pass filter) to f_2=56KHz (the cutoff frequency of low pass filter). Figure 18 shown the band pass filter circuit. Simulate the circuit at various frequencies (sweep the input frequency) to obtain a frequency response plot, figure 19 shown this plot, part of the hump will be pass (from f_1=48KHz to f_2=56KHz, outside of this range, the voltage would be very small in which can be neglect). Figure 20 shown a Bode plot of the circuit, the requirement is met, the dB atf_1 and f_2 are|H(j48000) |=-1.9dB, |H(j56000) |=-2.8dB, thus the difference is -0.9dB which is satisfied the requirement (-2 dB = 20?log?_10 (|H(f)|) = 2 dB for f_c–4000 = f = f_c+4000Hz).
Figure 18. Band Pass Filer
Figure 19. Band Pass Filter Frequency Response
Figure 20. Band pass filter Bode plot
Now that all the requirements for the band pass filter has met, hook the output of switching modulator to the band pass filter. However, OrCAD can only simulate up to three op-amps, because of that we had to have two separate projects, the first project simulated up to the switching modulator (Wien oscillator, signal generator, and switching modulator), the second project simulate the rest of the AM transmitter (band pass filer, power amplifier, antenna). In order to simulate the band pass filter with the first project, we need to export the voltage output of the first project (go to File ? Export and choose comma separated file). Open the exported file and delete the first row, the description row (the voltage source from file module won’t be able to read string value). Now replace the VAC source of circuit shown in figure 18 with the VPWL_FILE source, double click on <FILE> and insert the voltage output file exported earlier. Figure 21 shown the circuit thus far.
Figure 21. Band pass filter with switching modulator voltage input
Now we can simulate the band pass filer, figure 22 shown the output of the bandpass filter with 200Hzsignal generator input. Let’s measure the AM frequency (measure the time difference from positive peak to the next positive peak)8.7531ms-3.7581ms=4.995ms, thus the AM frequency is 1/4.995ms=200.2Hz, which is very close as expected (200Hz). Figure 23 is a zoom in of figure 22. From figure 23, we can measure the carrier frequency (same process as measure AM frequency), f_c=1/(2.5241ms-2.5048ms)=51813.5Hz, which is very close to the expect carrier frequency (51.85KHz). Both the AM frequency and carrier frequency are correct, thus the band pass filter is correctly designed.
Figure 22. BPF output of 200Hz signal generator input
Figure 23. Zoom in of figure 22 to find carrier frequency
Simulate the band pass filer with 4KHz signal generator input. Figure 24 shown the output of the bandpass filter with 4KHz signal generator input. Let’s measure the AM frequency (measure the time difference from positive peak to the next positive peak) 459.41µs-208.69µs=250.72µs, thus the AM frequency is 1/(250.72µs)=3988.51Hz, which is very close as expected (4000Hz). Figure 25 is a zoom in of figure 24. From figure 25, we can measure the carrier frequency (same process as measure AM frequency), f_c=1/(131.85µs-112.59µs)=51921.1Hz, which is very close to the expect carrier frequency (51.85KHz). Both the AM frequency and carrier frequency are correct, thus the band pass filter is correctly designed.
Figure 24.BPF output of 4KHz signal generator input
Figure 25. Zoom in of figure 24 to find carrier frequency
The system is successfully output an AM signal at both 200Hz and 4000Hz (the AM frequency and carrier frequency are correct), thus the system should be able to output a correct AM signal for any input frequency between 200Hz and 4000Hz. Hence, the requirement is met, we demonstrated successful sine wave output at both 200 Hz and 4 kHz.
Power Amplifier
The power amplifier consisted of two part, the non-inverting amplifier and class B output stage.Figure 26 shown the power amplifier circuit.
Figure 26. Power Amplifier circuit
First analyze the non-inverting amplifier, by putting voltage marker at the output of the op-amp, an amplified signal of the input can be obtained, figure 27 shown amplified signal of the input. Do a quick check, we know that the relationship of V_i and V_o of a non-inverting amplifier:
V_o=(1+R_2/R_1 ) V_i (6)
As you can see in figure 27, the output of the op-amp is not quite agreed with equation (6), because the op-amp does not have a feedback to the negative terminal. That explain the abnormal behavior. However, the input voltage does get amplified (by some gain close to the expected gain of a non-inverting amplifier), later when the OP-Amp has feedback from the class B output stage, the overall circuit would behave as expected (the feedback from the load is used rather than the feedback from the gate because it would reduce crossover distortion).
Figure 27. OP-AMP output
For a better understanding, let’s analyze the class B output stage alone, figure 28 shown the circuit of that will be used to analyze. Figure 29 shown the simulation of the circuit, as we can see that the output would be flat until the input voltage reach above0.5V, this is the threshold voltage, minimum voltage to turn on the transistor. After the threshold voltage, the output voltage increase as the input voltage increase, and the output voltage decrease as the input voltage decrease then flat out if input voltage less than 0.5V. We have two transistors (n-channel and p-channel), if the input voltage is positive (the gate voltage is positive) and above threshold voltage the n-channel transistor will conduct and the p-channel will be off, thus current will flow fromV_cc to ground and voltage drop across R_L would be positive. Oppositely, if the input voltage is negative (the gate voltage is negative) and below threshold voltage (less than -0.6V) the p-channel transistor will conduct and the n-channel will be off, thus current will flow from ground toV_cc and voltage drop across R_L would be negative. If the gate voltage is 0V then both transistors are off and the voltage drop across R_L will be 0V. This circuit operates in a push-pull fashion.
Figure 28. Class B output stage
Figure 29. Class B output stage simulation
Now let’s analyze the power amplifier as a whole. As shown in figure 26, the output from the OP-AMP connect to the class B output stage. The non-inverting amplifier will amplifier the input voltage (from the band pass filter), and the amplified voltage will connect to the gates of the class B output stage. As we all known, the larger voltage at the gate, the more current would flow the transistor which mean larger voltage across the load resistor, R_L. Then the load voltage will be feedback to the non-inverting amplifier. Figure 30 shown the simulation of circuit shown in figure 26. As shown in figure 30, the output is 5 time (the gain 1+ 4000?/1000?=5) larger than the input. Overall, the power of the input is amplified.
Figure 30. Power amplifier simulation
Now that the power amplifier is work as expected connect the output of the band pass filter to the positive terminal of the op-amp of the power amplifier, figure 31 shown this circuit. Figure 32 shown the simulation of the circuit with 200Hz signal input, and figure 33 shown the simulation of the circuit with 4000Hz. Both simulations behave as expected, they amplify the output of the band pass filter.
Figure 31. Power amplifier with band pass filter input
Figure 32. Amplified AM signal at 200Hz
Figure 33. Amplified signal at 4000Hz
Antenna
Now that the AM signal is created, filtered amplified and ready to send to antenna. The antenna job is to converts the electric power into radio wave. Figure 34 shown the complete AM transmitter circuit. Figure 35 show the radio AM radio wave at 51.85KHz carries a 200Hz tone. Figure 36 show the radio AM radio wave at 51.85KHz carries a 4000Hz tone. The AM radio wave can be analyzed (same process used in the band pass filter section).
For 200Hz:
Tone frequency: 1/(8.7531ms-3.7552ms)=200.084Hz
Carrier frequency:1/(131.85µs-112.59µs)=51921.1Hz
For 4000Hz:
Tone frequency: 1/(459.41µs-208.69µs)=3988.51Hz
Carrier frequency:1/(2.4084ms-2.3891ms)=51813.5Hz
For both message frequencies (the tone frequencies, 200Hz and 4000Hz),and the carrier frequency (51.85KHz) are really close to ideal case (message frequencies 200Hz and 4000Hz, carrier frequency 51.85KHz). Hence the theoretical part of the AM transmitter works as expect and met all the design requirements.
Figure 34. Complete AM transmitter circuit
Figure 35. AM radio wave at 51.85KHz carries a 200Hz tone
Figure 36. AM radio wave at 51.85KHz carries a 4000Hz tone
