# How to design AM modulator circuit using transistor

Theoretically, any electronic component that can create non-linear variation between the input and output can be used as a modulator. Diodes and transistors are non-linear devices since the the current is proportional to exponential of voltage. In the last tutorials How does Single Diode Modulator Circuit work? and Simple Amplitude Modulation (AM) circuit using Single Diode Modulator we explained and demonstrated how one can use a diode for signal modulation. Here we will show how to design AM modulator circuit using transistor.

See the following video demonstration of how transistor based AM modulator works.

The following is circuit schematic for amplitude modulation using BJT transistor.

In the above circuit BJT transistor BC107 is used as the amplitude modulator. This transistor based am modulator working mechanism is as follows. The two input signals are the modulating or message signal $$V_{m}$$ and carrier signal $$V_{c}$$. The equation representing these signals are as follows,

Modulating signal:

$$V_{m} = A_{m} Sin(2 \pi f_{m} t) = A_{m} Sin(w_{m} t)$$

Carrier signal:

$$V_{c} = A_{c} Sin(2 \pi f_{c} t) = A_{c} Sin(w_{c} t)$$

The frequency of the carrier signal is almost always much greater than the modulating signal. These two signal are mixed or summed by the resistor network R1 and R2. The summed signal before the coupling capacitor C2 is as follows,

$$V_{in} = V_{m} + V_{c}$$

or,

$$V_{in} = A_{m} Sin(2 \pi f_{m} t) + A_{c} Sin(2 \pi f_{c} t) = A_{m} Sin(w_{m} t) + A_{c} Sin(w_{c}t)$$

This summed or mixed signal $$V_{in}$$ enters into the transistor based AM modulator circuit via coupling coupling capacitor C2. The AM modulator transistor circuit is a voltage divider biased BJT amplifier with collector resistor replaced by LC tuned circuit. The values for the biasing resistors and coupling capacitors and bypass capacitor was calculated using the BJT Amplifier Design with Voltage Divider Biasing Online Calculator.

In the above am modulator circuit diagram, the collector current $$I_{c}$$ is given by,

$$I_{c} = I_{s} ( e^{\frac{V_{BE}}{ V_{T}}} - 1)$$

Since $$e^{\frac{V_{BE}}{ V_{T}}} >> 1$$

$$I_{c} = I_{s} e^{\frac{V_{BE}}{ V_{T}}}$$

Since that $$V_{BE} = V_{in}$$,

$$I_{c} = I_{s} e^{\frac{V_{in}}{ V_{T}}}$$

Using expansion of exponential function we can approximate,

$$I_{c} = a V_{in} + b V_{in}^2$$

where a and b are constant coefficients.

Therefore,

$$I_{c} = a (V_{m} + V_{c}) + b (V_{m} + V_{c})^2$$

on expansion of 2nd term,

$$I_{c} = a (V_{m} + V_{c}) + b (V_{m}^2+ 2 V_{m} V_{c} + V_{c}^2)$$

Using the trigonometric expressions for the modulating and carrier signals, we get,

$$I_{c} = a A_{m} Sin(w_{m} t) + a A_{c} Sin(w_{c} t) + b A_{m} Sin^2(w_{m} t)+ 2 b A_{m} A_{c} Sin(w_{m} t) Sin(w_{c} t) + b A_{c} Sin^2(w_{c}) t$$

Using trigonometric identity $$sin^2 A = 0.5(1-2 cos 2A)$$,

$$I_{c} = a A_{m} Sin(w_{m} t) + a A_{c} Sin(w_{c} t) + 0.5 b A_{m} (1-2 cos 2 w_{m} t)+ 2 b A_{m} A_{c} Sin(w_{m} t) Sin(w_{c} t) \\ + 0.5 b A_{c} (1-2 cos 2 w_{c} t)$$

or,

$$I_{c} = a A_{m} Sin(w_{m} t) + a A_{c} Sin(w_{c} t) + 0.5 b A_{m} - b A_{m} cos 2 w_{m} t+ 2 b A_{m} A_{c} Sin(w_{m} t) Sin(w_{c} t) \\ + 0.5 b A_{c}- b A_{c} cos 2 w_{c} t$$

or,

$$I_{c} = 0.5 b (A_{m} +A_{c}) + a A_{m} Sin(w_{m} t) + a A_{c} Sin(w_{c} t) - b A_{m} cos 2 w_{m} t \\ + 2 b A_{m} A_{c} Sin(w_{m} t) Sin(w_{c} t) - b A_{c} cos 2 w_{c} t$$

Utilizing trigonometric identity,   $$2 SinA SinB = Cos(A-B) - Cos(A+B)$$ we get,

$$I_{c} = 0.5 b (A_{m} +A_{c}) + a A_{m} Sin(w_{m} t) + a A_{c} Sin(w_{c} t) - b A_{m} cos 2 w_{m} t - b A_{c} cos 2 w_{c} t + b A_{m} A_{c} Cos[(w_{c} -w_{m}) t] \\ - b A_{m} A_{c} Cos[(w_{c} +w_{m}) t]$$

Thus the current flowing into the load resistor is,

$$I_{c} = 0.5 b (A_{m} +A_{c}) + a A_{m} Sin(2 \pi f_{m} t) + a A_{c} Sin(2 \pi f _{c} t) - b A_{m} cos 2 (2 \pi f_{m} t) - b A_{c} cos 2 (2 \pi f_{c} t) \\ + b A_{m} A_{c} Cos[2 \pi (f_{c} -f_{m}) t] - b A_{m} A_{c} Cos[2 \pi (f_{c} + f_{m}) t]$$

It consist of the following terms,

- The first term, $$0.5 b (A_{m} +A_{c})$$ 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 LC tank in the above BJT based AM modulator circuit diagram is used to filter the components other than the AM signal component. This LC resonant circuit is tuned to the carrier frequency of 10KHz. The value of the inductor and capacitor can be calculated using the LC resonant circuit online calculator

The following frequency spectrum shows the filtering action by the LC parallel resonant tank. In the spectrum we can see that all other components except the AM signal carrier signal component and the sum and difference signal of the modulating and carrier wave.

The same waveform of modulating signal of 1KHz, carrier signal of 10KHz and the output AM signal waveform on the amplitude modulation circuit using BJT BC107 is shown below.

Using Proteus Circuit Simulation Software we can view the signal waveform on oscilloscope as follows,

In this tutorial we showed how to build AM modulator using BJT transistor. To build AM modulator using FET transistor see the tutorial AM modulator using JFET transistor. One can test this circuit on breadboard by following the tutorial How to Build BJT amplifier and test with Soundcard based PC Oscilloscope.