# How does Single Diode Modulator Circuit work?

Single diode modulator is one of the simplest technique of achieving modulation. It is used in amplitude modulation which is one technique of transmission information wirelessly. Here it is explained how single diode modulator circuit works.

See the following video demonstration of how single diode modulator circuit works.

A simple practical single diode modulator circuit diagram is shown below.

The single diode modulator circuit is made up simple resistor network mixer(R1, R2) and the diode(D1). The modulating signal(Vm) and carrier signal(Vc) are applied to the resistive network mixer. Then the mixed signal enters the non-linear diode element. The diode causes non-linear mixing of the two input signal. The output from the diode mixer is a rectified am signal. For example if the modulating signal or message signal(Vm) is a sine wave of frequency 1KHz, carrier signal(Vc) is a sine wave of 4KHz then the resulting signal from the single diode mixer is a rectified amplitude modulated signal. The waveform at different stages is shown below.

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,

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

Then the input to the diode is the sum of these two signals,

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

or,

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

The modulation happens because a diode is non-linear device which obeys square law function. 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 that 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, $$0.5 b (A_{m} +A_{c})$$ 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.

These component at different frequencies can be viewed in frequency spectrum as shown below.

In proteus simulation software, using 1N4148 switching diode as in the above circuit diagram with modulating signal at 1KHz and carrier signal at 4KHz we obtain the following frequency spectrum

We can place an LC resonant circuit to filter out the modulating signal, intermodulation products and allow only the AM signal to pass. The circuit schematic for AM modulator using single diode is shown below.

As before, the modulating signal is a sine wave of 1KHz and the carrier signal is at 4KHz. The LC tank circuit is tuned at resonant frequency of 4KHz. The signal waveforms at different points in the circuit is shown below.

As can be seen in the above figure, the output waveform is largely attenuated. We can calculate the value of capacitor and inductor for LC parallel resonant circuit using the LC Parallel Resonant Circuit Online Calculator. If we use C1 of 10uF then L1 is theoretically 158.47uH.

The frequency spectrum at the output from the LC tank is shown below.

The output am signal from the LC resonant circuit is attenuated and hence must be amplified. That is why this single diode modulator is often referred as low level modulator. One way to amplify this amplitude modulated signal is by using operational amplifier like LM358 op amp. The next tutorial Simple Amplitude Modulation (AM) circuit using Single Diode Modulator explains how to amplify the AM signal.