Theory:
Amplitude modulation or AM is a method to transmit signals via electromagnetic transmission. It’s still used in radio systems to transmit audio signals although it has lesser in popularity compared to FM due to its lower signal to noise ratio.
What we do in AM, very roughly,is to “throw away” the frequency content of the message signal to a higher frequency. To understand how we do that, we need to utilise Fourier analysis techniques.
Before we go on, we must make a classification of AM’ed signals: Mainly there are two types AM: DSB-WC and DSB-C which stand for Double side band modulation without carrier and double side band modulation with carrier. In this paper, we’ll utilise DSB-C because of its ease of demodulation. However we also introduce DSB-WC because it forms the basis for DSB-C. In effect, DSB-C is nothing more than a mere extension of DSB-WC.
Double side band modulation without carrier:
Let us have a message signal m(t). And let M(w) be the Fourier transform of m(t). In time domain we multiply m(t) with cos(wct). Where wc stands for the angular carrier frequency. What we do in frequency domain is that we actually convolve M(w) with two dirac deltas located at frequencies +wc and -wc. Here is the pictorial description:
Double side band modulation with carrier:
The only difference of DSB-C is that we add a carrier to the modulated signal. So the modulated signal will become (m(t) + A)cos(wct) . The reason why we add a carrier is for the sake of ease of demodulation: If we can avoid m(t) to cross the time axis, we can preserve the envelope in the modulated signal, and demodulate it simply via using a simple circuit called envelope detector.
Here is the pictorial depiction of the situation:
Let us have a zero-crossing message signal m(t):
It’s clear that we can’t store envelope information in the modulated signal m(t)cos(wct) .
So we add a carrier component with amplitude A, and here is the time and frequency domain picture of the modulated signal:
But we should keep in mind that this scheme hold if the condition A + m(t) > 0 holds. Otherwise we will lose the envelope information and this modulation effort will become meaningless since it will be no different than a normal DSB-WC modulation and we won’t be able to use a simple envelope detector to demodulate this signal. Instead, we would have to use a local oscillator to demodulate the signal. It won’t be favorable since this way, the receiver has to “know” the carrier frequency and then things will be complicated.
Implementation:
Modulation:
As we mentioned before, we’ll use DSB-C modulation because of its ease in demodulation. Here is the circuit used for modulation and it’s simulation:
Source called V1 generates the message to be transmitted. It’s amplitude is 5V and frequency is 1kHz. The circuit’s working principle is as follows: As we can see we have a simple common emitter amplifier topology because of the bypass capacitor connected to the emitter of the transistor Q1, as far as the small signal operation is considered. But the thing is, because we connected the message signal to the branch by-passed by a capacitor, we constantly change the biasing point of the transistor Q1 according to our message signal. So we can say that we have a variable gain since the transconductance of Q1 varies. We have the following output at the collector of the Q1:
Then we high-pass filter it with the capacitor C3. And we get the following output: (Here we also demonstrate the message signal- The signal with higher amp. is the message signal)
So we see that we have successfully modulated the message signal.
Demodulation:
As we had mentioned, we use an envelope detector to accomplish this task. This is the envelope detector circuit:
As can be seen this is a super simple circuit.
To understand it, we may divide it into two blocks:
-Main Envelope detector; an half wave rectifier with a filter capacitor (diode D4, resistor R8 , capacitor C6)
-An high pass filter (capacitor C7, resistor R9)
Main envelope detector:
With diode D4 and the resistor R4 we half wave rectify the the signal. Then with the filter capacitor we try to follow the envelope of the signal. The crucial point when designing this circuit is that we have to choose RC time constant so that, it is not too small to avoid excessive discharges between peaks, and we don’t have to choose it too large, to make it possible for the capacitor to follow the signal. To summarize here is the interval in which we have to choose the RC time constant:
1/wc < < RC < 1/(2πB) where B is the bandwidth of the message signal.
So let us do the calculation:
0.796us<<RC <0.6ms – we chose RC as 1k ohm * 0.15uF = 0.15ms – so we satisfied the constraint.
High pass filter:
Simple high pass filter with 3dB cut-off approximately 800Hz.
Here are the simulation results:
The waveform above is the output of the rectifier with filter capacitor. We then remove the DC component with the high pass filter (you may also call it DC-blocker) and get the waveform below.
However, these waveforms didn’t satisfy me, and I tried something different; I removed the diode D4 from the envelope detector. Here is the new circuit and waveform demodulated: (Obviously, this demodulation scheme would not work for all signals; we remove the diode just for illustration purposes: In the final design we have indeed a series connected diode to capacitor C3.
I suspected the diode because of its non-linear behaviour. This is the result I get after I remove it from the circuit:
(It’s the waveform at the node indicated by a probe on schematic above)
The waveform we get now is much more sine-like.
So I can conclude that, because of the non-linear behaviour of the diode, our waveform get distorted. To solve this issue, a higher voltage carrier can be applied, so that diode has lesser relative voltage drop on it. But to accomplish, this VCC supply voltage must be increased so that we stay in the linear region of operation of our transistor.
I will finalize the discussion with the spice code of the circuit:
Q_Q1 5 2 4 BC548A
C_C1 1 2 100n
R_R3 2 6 56k
R_R2 5 6 10k
V_V3 6 0 30V
C_C2 0 4 100n
R_R4 0 2 15k
V_V2 1 0
+SIN 0 20m 200k 0 0 0
R_R11 0 8 1k
C_C3 5 9 470p
D_D1 7 9 diode
C_C8 0 7 0.15u
C_C9 8 7 0.200u
R_R1 3 4 4.7k
R_R10 0 7 1k
V_V1 3 0
+SIN 0 5 1k 0 0 0
.tran 1us 4ms
.probe
.END
References:
Modern Digital and Analog Communications Systems, B.P. Lathi, Zhi Ding, 3/e
http://www.zen22142.zen.co.uk/spice/ammod.htm
Maze of amazement 
good explanation..