AM MODULATION/DEMODULATION

Written For:

Prof. Ray Kwok

EE 172

Written By:

Chad Schrader

Benjamin Dubois

Omar Castillo

Ryan Clarke

Efrem Habte

Farial Mahbub

Introduction:

(Written by Efrem Habte)

Our group is the Modulation/Demodulation/Mixer group. The purpose of this project is to modulate and demodulate an AM signals. There are different ways of modulating and demodulating AM signals. This project is done with the simplest design available while maintaining the desired high frequency signal. T

Modulation

(Written By Ryan Clarke)

Modulation is a technique used for encoding information into a RF channel. Typically the process of modulation combines an information signal with a carrier signal to create a new composite signal that can be transmitted over a wireless link. In theory a message signal can be directly sent into space to a receiver by simply powering an antenna with the message signal. However, message signals typically don't have a high enough bandwidth to make direct propagation an efficient transmission technique. In order to efficiently transmit data, the lower frequency data must be modulated onto a higher frequency wave. The high frequency wave acts as a carrier that transmits the data through space to the receiver where the composite wave is demodulated and the data is recovered. There are a few general types of modulation; Frequency Modulation (FM), Phase Modulation (PM), and Amplitude modulation (AM). Frequency modulation encodes data by performing shifting of frequency, phase modulation performs shifts in phase, and amplitude modulation controls the envelope of the carrier wave. AM is usually the simplest to implement and is thus the scheme we chose for our modulator.

In an AM radio system a high frequency sinusoidal wave is amplitude modulated by a lower frequency message signal.

This can be expressed by

V_am(t) = [(A + V_m(t))] Cos(2πf_ct)

where Cos(2πf_ct) is the carrier frequency and V_m(t) is the modulating signal. In our application f_c = 915 MHz and V_m(t) = Audio Signal. We can take Vm(t) = V_mCos(2πf_mt) where f_m = highest frequency component in the message signal. For transmitting audio, f_m = 20 kHz. The constant "A" is chosen such that V_am(t) never becomes negative. Thus V_am(t) can be modified to

V_am(t) = A[(1 + mCos(2πf_mt))] Cos(2πf_ct).

In this expression "m" is known as the modulation index. After performing the multiplication of the modulated signal the spectral output can be determined.

V_am(t) = A[(Cos(2πf_ct) + mCos(2πf_mt) Cos(2πf_ct))]

V_am(t) = A[(Cos(2πf_ct) + m/2[Cos(2π(f_c-f_m)t) + Cos(2π(f_c+f_m)t))]]

From the multiplication it is evident that the resulting spectrum consists of the center frequency f_c and two side band frequencies (f_c - f_m) and (f_c + f_m).

What has occurred is that the low frequency message signal has been translated to a much higher frequency range for greater transmission efficiency. Either of the side bands can be used to recover the message signal at the demodulator. One simply needs to filter out the unwanted side band before sending the signal to the demodulation stage. This modulation scheme is typically implemented in circuitry by a component called a Double-Side-Band mixer. The mixer physically multiplies the carrier wave, driven by an oscillator, with the message signal to produce the AM signal.

Diode Double Balanced Mixer

(Written by Chad Schrader)

Our group implemented the modulator by using a diode double-balanced mixer design. We decided to use this design because it seemed like it would be the most straightforward. The mixer basically consists of two balanced to unbalanced transformers (baluns) and a Schottky diode quad. The Schottky quad basically is a rectifier that multiplies the local oscillator input (915 MHz) and the audio input (20 kHz). We implemented the Schottky quad by putting four Schottky diodes in a ring formation. The two baluns are used to match the circuit to the external circuits that are connected to the mixer. We made our own baluns by buying some toroidal ferrite cores and #32 wire and wrapping the cores according to a schematic for a 1:1 balanced to unbalanced transformer found in the ARRL Handbook. The cores were wound using three wires twisted together. There were 7 winds on the toroid in total. This circuit was constructed on a protoboard, taking care to try to keep the leads between components as short as possible. SMA connectors were used for interfacing with the other circuits in the transmitter.

Envelope Detector

The demodulator was implemented using an envelope detector circuit. This consists of a diode and a low pass filter circuit. The low pass filter circuit is simply a capacitor and a resistor in parallel. The values for the resistor and the capacitor were calculated using the following equation:

where is the local oscillator frequency (915 MHz) and is the frequency of the audio signal (20 kHz). Once we found a value for RC (), we assumed a value of 1000 for R. This gave us a value of 23 pF for C. In our implementation of the circuit, we used a 24 pF capacitor because that was the closest standard value. The circuit was constructed on a protoboard, again trying to keep the leads between components as short as possible. We also used SMA connectors for the input and output of this circuit.

Demodulator and Envelope Detector

(Written by Farial Mahbub)

Amplitude Modulation (AM) refers to the method of adjusting an electromagnetic carrier frequency by varying its amplitude in accordance to the analogue signal to be transmitted.There are two essential methods that are used to demodulate AM signals and in this portion of the report we will discuss both. The figure below represents the circuit used as the Demodulator in this project.

The first method of demodulation is using the envelope detector. The envelope detector is essentially made up of a rectifier and a low pass filter (see figure below). In this project a diode was used as the rectifier to pass current in one direction only. In order to calculate the value of the RC time constant to be used, the following equation is used:

2πf_C >> 1/(RC) > 2πf_m

V_r = V_p (1 –e ^-1/fcRC)

where f_C and f_m are the carrier frequency and the modulated frequency respectively. The reason the inverse of the time constant is significantly smaller than the carrier frequency is to keep the ripple created minimal. The second equation shown above defines the peak-to-peak value of the ripple, V_r of the rectified signal and where V_p is the peak value of the incoming signal and f_c is the frequency of the signal.

The second method for demodulation that we did not choose to implement is the product detector. This circuit essentially multiplies the incoming signal by the signal of a local oscillator which is at the same frequency and phase as the carrier signal. After filtering the product, only the original audio signal remains (works for AM as well as Single Side Band Modulation, SSBM).

The output of the above described circuits can be seen graphically in the figure below. The Signal 1 is the modulated signal that is applied to the Detector. The diode present in the circuit demodulates the AM signal by allowing its carrier to multiply with its sidebands. The diode passes current in only one direction and its output voltage is proportional to the square of its input voltage. Thus, if an input voltage that varies according to the modulation envelope is used, the information present in the sidebands would be successfully recovered. Once the signal is rectified (after it passes through the diode), it resembles Signal 2. The next component in the circuit is the low-pass filter (the resistor and capacitor in parallel) and this filters out the RF and turns it into Signal 3. The coupling capacitor in the circuit is present to eliminate the DC component in the received signal thus centering the information signal around the zero axis as in Signal 4.

Measurements, Testing, and Calculations of the Amplitude Modulator

(Written By Omar Castillo)

A plot of Power S one sideband (dBc) against modulation index(m) for DSB-LC is shown below.

M	S(dBc)
0.1	-26.02
1	-6.02
2	0.0006

Testing the Sidebands

We arbitrarily set the carrier signal to 30kHz to make the sidebands as close to equal as we can make them. With the carrier signal set at 30kHz, a 3kHz 10Vpp sinusoidal signal was sent through the input port where audio would be inputted and the sidebands were measured.

f_c = 30kHz

	fc + 3kHz	fc - 3kHz
Power	45.55dBm	45.16dBm

Double Sideband Suppressed Carrier (DSB-SC) Modulation.

With the carrier signal set at 30kHz, we input signal at 3 kHz, 10Vp-p sinusoidal without DC offset signal being applied. Scope and spectrum analyzer measurements were taken at the output.

f(kHz)	P(dBm)
27	-22.71
33	-23
86.2	-53.3
92.6	-56.9

The measured spectrum of the DSB-SC is comparably close to the theoretical model.

We now varied the input signal and tested the output. The input modulating signal amplitude was varied and both the input and output voltage were measured.

Vin,pp(V)	Vo,pp(V)
0	0
2	0.8
4	1.5
6	2.3
8	3
10	4

The modulating signal (input signal) and the output amplitudes are proportional by the amplitude of the carrier frequency.

Keeping the input amplitude constant at 10Vpp, we varied the frequency of the modulating input signal from 4kHz to 10kHz in increments of 2kHz and measured corresponding amplitudes.

f(kHz)	Vo,pp(V)
4	9.5
6	9.5
8	9.5
10	9.5

From the data it appears that the frequency of the modulating signal does not affect the output amplitude.

Double Sideband Large Carrier (DSB-LC) Modulation

We now apply a DC Offset to get a DSB-LC signal. On adding DC offset to the input we get an equation of the form [A + f(t)] which forms basic form of DSB-LC, i.e [A + f(t) ]cosω_ct.

We continue to use an input modulating signal of 3kHz, 2Vp-p sinusoidal with a +2V DC offset. Measurements of the output were taken on both the oscilloscope and spectrum analyzer. Data of the spectrum was taken twice, once with a span from 0-120kHz and another with a span of 10-50kHz.

f(kHz)	P(dBm)	f(kHz)	P(dBm)
27	-36.4	26.6	-36.64
30	-24.6	29.6	-24.4
33	-36.8	32.7	-36.9
86.2	-67.07
89.2	-56.3
92.2	-70.08

Comparing the spectrum of the DSB-LC with the theoretical model, they are almost the same.

Looking at the modulated signal at the output, we obtained values for Emax and Emin and computed the modulation index.

Emax = 2.2Vpp m = 0.468

Emin = 0.8Vpp

The input amplitude at the carrier input was varied from 0-10Vpp in 1V increments and measurements of the max and min energies were taken from the oscilloscope and the power of the carrier and two sidebands were taken from the spectrum analyzer. Values of m and S were calculated from the energies and power values.

Vi,pp(V)	Emax(V)	Emin(V)	Pl(dBm)	Pc(dBm)	Pr(dBm)	m	S(dBc)
0	1.6	1.5	-56.3	-24.3	-56.6	0.032258	-32.15
2	2.2	1.9	-37.09	-24.4	-37.4	0.073171	-12.845
4	1.9	0.1	-31.1	-24.8	-31.4	0.9	-6.45
6	3.6	-0.8	-27.1	-24.9	-27.5	1.571429	-2.4
8	4.2	-1.6	-24.6	-25.1	-25.13	2.230769	0.235
10	4.9	-2.3	-22.7	-25.3	-23	2.769231	2.45

Pl = left sideband power

Pc = Carrier power

Pr = right sideband power

Plotting the modulation index vs. the input amplitude, the data shows that there is a linear relationship. This makes sense since the input amplitude has a direct relationship with Emax and the values of the m were calculated from the Emax and Emin values.

Looking at the graph for sideband power vs. modulation index, it looks close to theoretical models.

Using a 3kHz, 2Vpp sinusoidal signal as our input, the DC offset was varied from -6 to +6V in 1V increments. Measurements were taken from the oscilloscope of Emax and Emin and the modulation indices were calculated.

DC Offset (V)	Emax(V)	Emin(V)	m
-6	5.2	4	0.130435
-5	4.5	3.2	0.168831
-4	3.8	2.4	0.225806
-3	3	1.7	0.276596
-2	2.3	0.9	0.4375
-1	1.6	0.1	0.882353
0	0.8	0	1
1	1.8	0.1	0.894737
2	2.3	1	0.393939
3	3	1.7	0.276596
4	3.8	2.5	0.206349
5	4.5	3.3	0.153846
6	5.1	3.9	0.133333

The relationship between the modulation index and the DC offset seems to be of an exponential relation. That is m = e^-k|x|, where x is dc offset and k is a con

Problem Analysis:

(Written By Benjamin J. S. Dubois)

1. Problem with radiation of circuit boards:

· How does radio work?

If you shake ("accelerate") an electrically charged object, it radiates radio ("electromagnetic") waves through space. 60 Hz power lines don't radiate much, a 1 Gigahertz printed-circuit board wire radiates enough to be a bother. (http://comsec.com/wiki?HowToRF)

This quote expresses the fundamental issue with our circuit: at 915 MHz close to 1GHz each connecting lines will radiates electromagnetic waves. Hence our circuits create interferences. A near perfect circuit would use substrates, or copper tapes instead of wires.

2. Problem with DSB-LC AM:

There are various forms of Amplitude Modulation

1. Conventional Amplitude Modulation (Alternatively known as Full AM or Double Sideband Large carrier modulation(DSB-LC)

2. Double Sideband Suppressed carrier(DSB-SCS) modulation

3. Single Sideband (SSB) modulation

4. Vestigial Sideband (VSB) modulation

We are using DSB-LC.

Over-Modulation with DSB-LC:

In the Testing section, the modulating index m is merely defined as a parameter, which determines the amount of modulation. However, we have to ask ourselves a question of what is the degree of modulation required to establish a desirable AM communication link?

The answer to the question is to maintain m < 1.0(100%).

This is important as to ensure successful retrieval of the original transmitted information at the receiver end. Note that by performing the demodulation process (reverse of modulation) the message signal is simply being traced out from the envelope of the modulated signal. To have a quick recap, amplitude of the modulated signal varies in proportion to the amplitude of the information signal.

Thus, once m > 1.0(100%), envelope distortion will occur and the waveform is said to be overmodulated. Under this circumstances, is large enough, resulting the non-proportionality of ----hence distortion of the desire message signal!!

Ac: DC component of Amplitude of carrier signal; s(t) is AM signal; is modulation signal.

(http://foe.mmu.edu.my/course/etm3046/notes/AM(-DSSC)ETM2042.doc; Chapter 3 Amplitude modulation H Communications I -ETM2042)

3. Problem with Demodulation: (using an Envelop detector)

a Rectifier with a Filter Capacitor= The Peak Rectifier

We can avoid negative peak clipping by choosing a small value of. However, to

minimize ripple we want to make as large as possible. In practice we should therefore

choose a value to minimize the signal distortions caused by these effects. This is clearly only possible if the modulation frequency.

Envelope detectors only work satisfactorily when we ensure this inequality is true.

RC is too close to inverse of modulation frequency, excessive ripples but no negative peak.

RC is too close to inverse of modulation frequency, less ripples but significant negative peak

”Just” middle when RC is at average on log scale between inverses of carrier and modulation frequencies.

Construction of the Demodulator Circuit:

(Written by Efrem Habte)

Since the frequency that we are using for the project is very high (915MHz) the first thing that we have to put on mind is how we can reduce the power loss and distortion. When constructing this circuit we tried of using high frequency board that we can find (FR4). We cut the leads as short as possible and solder them to the board to reduce distortion and power loss.

Another Equation that we use also for checking is

2Πf_c = 1/R₃C₂ > 2Πf_m

Where f_c is a carrier frequency and f_m is the modulating frequency.

Using this equation you have to basically play around with the values of the resistor and capacitor until you get the frequency required.

Why we make the leads short:

Distortion is a signal due to non-linearity in the circuits. In order to have a good circuit of the system we should introduce as little distortion as possible. The reasons for distortion come from long leads and from inside of the manufacturing component. An example is a Thermal noise, which is a noise created by the resistor.

Conclusion:

In this project we implemented a AM modulator and demodulator. We implemented the modulator by using a diode double balanced mixer. The demodulator was implemented using a envelope detector. The mixer circuit was tested using a spectrum analyzer. We also discovered some of the limitations of our circuit design.