# AM modulator using BJT Transistor

AM modulation circuit is a circuit in which a modulating signal amplitude varies the carrier wave amplitude. This is used in wireless AM transmitter where low frequency modulating signal is embedded into high frequency carrier signal. An AM modulator circuit can be build using diodes or transistors(BJT and FET transistors). Here an AM modulator design using BJT(Bipolar Junction Transistor) is illustrated.

Shown below is one way constructing low power AM modulator.

In this BJT AM modulator circuit we have used BC107 BJT transistor. The BJT is biased using voltage divider biasing method and the value of the biasing resistor(R1,R2 and R4) were calculated using the online BJT amplifier design calculator

The modulating signal can be mathematically expressed in the following way.

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

where $$w_{m}=2 \pi f_{m} t$$ is the frequency and $$V_{m}$$ is the amplitude of the modulating signal.

This modulating signal is coupled into the base of the BJT mixer via the coupling capacitor C2. Here the modulating signal frequency is taken as 1KHz and the amplitude is 500mV.

Similarly, the carrier signal often referred as local oscillator signal can be expressed as a sine wave of frequency $$w_{c}=2 \pi f_{c} t$$ and amplitude $$V_{c}$$,

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

This carrier signal enters into the BJT mixer via the emitter through the coupling capacitor C3. Here the carrier signal frequency is taken as 10KHz and the amplitude is 800mV.

The collector current of the mixer circuit contains the AM signal with intermodulation products. The LC resonant tank formed by the capacitor C1, inductor L1 and internal wire resistance R1 is tuned at the AM signal frequency which is same as that of the carrier signal which is 10KHz in this case. The value of the LC resonant components were calculated using the online LC resonant tank calculator. The LC parallel tank is a band pass filter which allows signals within certain frequency range to pass through it and blocks other frequency signals. The output is coupled to the load resistor RL via the output coupling capacitor C4.

The following shows modulating signal, carrier signal and the AM signal waveform on a oscilloscope.

As can be observed from the above oscilloscope setting, the amplitude of the AM signal is very low compared to the modulating and carrier signal. Hence such circuits are also called low level AM modulators.

As was explained in the previous tutorial AM modulator using JFET transistor, the modulating signal varies with carrier signal peak amplitude as reference point. The following shows AM signal waveform

From the above AM signal waveform diagram, we can notice that the modulating signal waveform varies below and above the carrier signal amplitude peak instead of the zero reference while the carrier signal waveform varies in reference to the zero voltage reference. Because of this the relative amplitude of the modulating and carrier signal is important. That if the amplitude of the carrier signal is lower than the amplitude of the modulating signal then a distorted AM signal results. Thus there is condition for generating AM signal which is that the amplitude of the carrier signal must be higher than the amplitude of the modulating signal. Mathematically

$V_{c} > V_{m}$

Explained above, the amplitude of the AM wave is given by,

$V_{am} = V_{c}+ v_{m} = V_{c}+ V_{m} Sin(w_{m} t)$

Thus the AM signal can be mathematically written as,

$v_{am} = V_{am} Sin(w_{c} t) = (V_{c}+ V_{m} Sin(w_{m} t)) Sin(w_{c} t)$

Defining modulation index m as,

$m= \frac{V_m}{V_c}$

and since $$V_c$$ > $$V_m$$ for distortionless AM we must have modulation index m < 1.

We can rewrite the above am signal equation as,

$v_{am} = V_{c}(1+ m Sin(w_{m} t)) Sin(w_{c} t)$

This is the standard equation of AM signal.

This AM signal appears in the load resistor RL via the output coupling capacitor C4. The above equation of AM signal can be further factored into the following equation.

$v_{am} = V_{c} Sin(w_{c} t) + m V_{c} Sin(w_{m} t) Sin(w_{c} t)$

or,

$v_{am} = V_{c} Sin(w_{c} t) + \frac{m V_{c}}{2} \{Cos((w_{m}+w_{c}) t) + Cos((w_{c}-w_{m}) t)\}$

or,

$v_{am} = V_{c} Sin(w_{c} t) + \frac{m V_{c}}{2} Cos((w_{m}+w_{c}) t) + \frac{m V_{c}}{2} Cos((w_{c}-w_{m}) t)$

That is AM signal consist of a carrier wave(the first term), sum and difference in frequency terms(the second and third). We can verify this plotting the spectra of the output AM signal at the load resistor using spectrum analyzer as shown below.

As you can see in the above frequency spectrum graph, the signal consist of a 10KHz signal which is the carrier and the 9KHz signal which is the difference and the 11KHz signal which is the sum of the modulating and carrier signal as indicated by the standard AM signal equation.

In this tutorial we have explained how AM modulator using BJT Transistor works. There are other methods of designing AM modulators whose tutorial links are provided below.