In this electronics circuit tutorial, we show how to design Simple amplitude modulation circuit using Single Diode Modulator. The following is the AM modulator circuit diagram designed with single diode and operational amplifier.
The modulating signal can be written as,
\( V_{m} = A_{m} Sin(2 \pi f_{m} t) = A_{m} Sin(w_{m} t) \)
And the carrier signal can be written as,
\( V_{c} = A_{c} Sin(2 \pi f_{c} t) = A_{c} Sin(w_{c} t)\)
These two signals are added in the using the resistor network. The added signal enters the diode D1.
\( V = V_{m} + V_{c} \)
or,
\( V = A_{m} Sin(2 \pi f_{m} t) + A_{c} Sin(2 \pi f_{c} t) \)
The diode is non-linear device which obeys square law function(approximately). That is the output current from the diode is non-linearly related to voltage across it and is approximately given by,
\( I = a V + b V^2 \)
where a and b are coefficients.
The first term \(a V\) is linear component which is usually the DC bias. The second term \(b V^2 \) is second-order or square-law component of the current which causes the modulation.
Replacing V in the above equation we get,
\( I = a (V_{m} + V_{c}) + b (V_{m} + V_{c})^2 \)
on expansion of 2nd term,
\( I = a (V_{m} + V_{c}) + b (V_{m}^2+ 2 V_{m} V_{c} + V_{c}^2) \)
Using the trigonometric expressions for the modulating and carrier signals, we get,
\( I = a A_{m} Sin(w_{m} t) + a A_{c} Sin(w_{c} t) + b A_{m} Sin^2(w_{m} t)+ 2 b A_{m} A_{c} Sin(w_{m} t) Sin(w_{c} t) + b A_{c} Sin^2(w_{c}) t \)
Using trigonometric identity \( sin^2 A = 0.5(1-2 cos 2A)\),
\( I = a A_{m} Sin(w_{m} t) + a A_{c} Sin(w_{c} t) + 0.5 b A_{m} (1-2 cos 2 w_{m}
t)+ 2 b A_{m} A_{c} Sin(w_{m} t) Sin(w_{c} t) \\ + 0.5 b A_{c} (1-2 cos 2 w_{c}
t)
\)
or,
\( I = a A_{m} Sin(w_{m} t) + a A_{c} Sin(w_{c} t) + 0.5 b A_{m} - b A_{m} cos 2 w_{m} t+ 2 b A_{m} A_{c} Sin(w_{m} t) Sin(w_{c} t) \\ + 0.5 b A_{c}- b A_{c} cos 2 w_{c} t \)
or,
\( I = 0.5 b (A_{m} +A_{c}) + a A_{m} Sin(w_{m} t) + a A_{c} Sin(w_{c} t) - b A_{m} cos 2 w_{m} t \\ + 2 b A_{m} A_{c} Sin(w_{m} t) Sin(w_{c} t) - b A_{c} cos 2 w_{c} t \)
Utilizing trigonometric identity, \( 2 SinA SinB = Cos(A-B) - Cos(A+B) \) we get,
\( I = 0.5 b (A_{m} +A_{c}) + a A_{m} Sin(w_{m} t) + a A_{c} Sin(w_{c} t) - b A_{m} cos 2 w_{m} t - b A_{c} cos 2 w_{c} t \\ + b A_{m} A_{c} Cos[(w_{c} -w_{m}) t] - b A_{m} A_{c} Cos[(w_{c} +w_{m}) t] \)
Thus the current flowing into the load resistor is,
\( I = 0.5 b (A_{m} +A_{c}) + a A_{m} Sin(2 \pi f_{m} t) + a A_{c} Sin(2 \pi f _{c} t) - b A_{m} cos 2 (2 \pi f_{m}
t) \\ - b A_{c} cos 2 (2 \pi f_{c}
t) + b A_{m} A_{c} Cos[2 \pi (f_{c} -f_{m}) t] - b A_{m} A_{c} Cos[2 \pi (f_{c} + f_{m}) t]
\)
It consist of the following terms,
- The first term, \( I = 0.5 b (A_{m} +A_{c}) \) which is DC signal that is easily removed by filtering
- The term \(a A_{m} Sin(w_{m} t)\) is the modulating(message) signal which is not required and can be filtered out easily as the carrier signal frequency is much higher than the modulating signal frequency.
- The third term, \(a A_{c} Sin(w_{c} t)\) is the carrier signal which is key part in AM signal.
-
The fourth term \(b A_{m} cos 2 (2 \pi f_{m}
t)\) and the fifth term, \( b A_{c} cos 2 (2 \pi f_{c}
t) \) are the 2nd harmonic of modulating and carrier signal which is at
twice the frequency of the original signals. Such harmonic components
are called Intermodulation Products and are not required and are
filtered out.
- The sixth and seventh terms \(b A_{m} A_{c} Cos[2 \pi (f_{c} -f_{m}) t] - b A_{m} A_{c} Cos[2 \pi (f_{c} + f_{m}) t]
\) are the sum and difference signal of the modulating and carrier wave. These are part of modulated wave.
The output from the diode is modulated signal that contains along with AM signal and also harmonic or intermodulation products as well as DC signal and input modulating and carrier signal. The output from the diode is given by,
\( I = 0.5 b (A_{m} +A_{c}) + a A_{m} Sin(2 \pi f_{m} t) + a A_{c} Sin(2 \pi f _{c} t) - b A_{m} cos 2 (2 \pi f_{m} t) \\ - b A_{c} cos 2 (2 \pi f_{c} t) + b A_{m} A_{c} Cos[2 \pi (f_{c} -f_{m}) t] - b A_{m} A_{c} Cos[2 \pi (f_{c} + f_{m}) t] \)
The intermodulation products(harmonics) and other unwanted signals other than the AM signal can be removed by filtering using LC resonant circuit. The resonant circuit component values for L1 and C1 are selected to the carrier signal frequency. If the modulating signal frequency is 1KHz and the carrier signal frequency is 10KHz then the resonant frequency of the LC circuit is 10KHz. We can use the LC Parallel Resonant Circuit Online Calculator to calculate the inductor L1 and capacitor C1 values. This is as shown below.
After the LC resonant tank the output signal after the tank circuit is given by,
\( I = a A_{c} Sin(2 \pi f _{c} t) + b A_{m} A_{c} Cos[2 \pi (f_{c} -f_{m}) t] - b A_{m} A_{c} Cos[2 \pi (f_{c} + f_{m}) t] \)
The following is frequency spectrum of the signal after the LC resonant circuit.
After the LC resonant circuit, two LM358 op-amp amplifier are used to amplify the amplitude modulated signal. This is because when signal is passed through the LC tank the signal is attenuated. This amplitude modulation circuit using op amp circuit is shown below.
The amplifying circuit is designed using LM358 with single supply voltage(see How to power op-amp with dual supply using single supply?).
The input signal waveform and output amplitude modulated signal is shown in the following AM modulator circuit diagram.
Below picture shows am modulator circuit signal waveform on oscilloscope obtained using simulation in Proteus electronics design software.
The following video demonstrates how amplitude modulation circuit constructed using single diode modulator and op-amp amplifier works.
So in this tutorial we showed how to design Simple Amplitude Modulation (AM) circuit using Single Diode Modulator. We can also design AM modulator using two diodes, four diodes and BJT or FET transistors. See the following tutorial for this.
- How Two Diode Single Balanced Mixer Design Works
- How to design balanced mixer with two diodes
