AM modulator is an electronics circuit that impresses message signal or modulating signal onto a carrier signal. In AM modulator, the high frequency carrier signal amplitude is varied in accordance with the message signal amplitude which has lower frequency, hence the name Amplitude Modulation. AM modulator is used in AM transmitter for generating AM signal. There are many ways in which we can build an AM modulator circuit such as which is listed and explained briefly in the article different types of AM modulator and demodulator circuits. In this article it is shown one another way of building AM modulator circuit that uses two bipolar junction transistors(BJT).

## AM modulator circuit using Two BJT Transistor

The following shows AM modulator circuit using two BC107 BJT Transistor.

Here the working of this AM modulator circuit is shown to work with 100KHz carrier frequency. In the above circuit diagram the VM and VC are two function generators that generates audio signal(or the message signal) and the carrier signal respectively. The message signal VM is connected to the base of the BC107 Q1 transistor via the 10Kohm potentiometer and coupling capacitor C1=0.1uF. To start with we will use input modulating signal of 1KHz with 1.5V amplitude or so. The R1=100KOhm and R2=6.8KOhm resistors are used to bias the Q1 transistor and establish the dc quiescent point.The message signal fed to the junction of these resistors causes the bias to vary. R3 is the emitter resistor for the transistor Q1 which is also the collector resistor for Q2. The carrier signal of 100KHz and initial amplitude of 3V is applied to the base of the transistor Q2 via the 10KOhm potentiometer and the coupling capacitor C2. The resistor R4=10KOhm is used bias the bipolar transistor Q2. The carrier signal that enters the base of Q2 is amplified and modulated with the message signal at the Q2 collector. In actual AM transmitter, the carrier signal can be generated using LC oscillator like Colpitts oscillator or Hartley oscillator or use crystal oscillator like Pierce crystal oscillator circuit. The modulated signal is then passed into the LC band pass filter consisting of the capacitor C3=1nF and L1=2.5mH via the output coupling capacitor C4=1nF. The value of the band pass filter capacitor and inductor are selected such that the center frequency of 100KHz, that is the band pass filter center frequency is equal to the carrier signal frequency which is 100KHz in this demonstration. One can use the This modulator circuit is similar to emitter AM modulator circuit.

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

**Mathematics of Amplitude Modulation(AM) **

The standard form of AM wave is described by the following equation.

\(s(t)=[1+k_a m(t)]c(t)\) ----------------->(1)

where, ka is the amplitude sensitivity of the AM modulator, m(t) is the modulating signal and c(t) is the carrier signal.

Let \(m(t)=A_m cos(w_m t)\)

and \(c(t)=A_c cos(w_c t)\)

Then we have,

\(s(t)=[1+k_a A_m cos(w_m t)]A_c cos(w_c t)\) ----------------->(2)

The AM envelope is defined as,

\(a(t) = A_c |1+k_a A_m cos(w_m t)|\) ----------------->(3)

Thus the AM wave can be written in terms of envelope as,

\(s(t)=a(t) cos(w_c t)\) ----------------->(4)

That the circuit presented above generated standard AM or conventional AM signal with carrier signal and upper plus lower modulated signal can be verified using the spectrum analysis of the AM signal. This is shown below.

**Modulation factor and Modulation percentage **

Let, \(\mu = k_a A_m\) ---------------->(5)

where \(\mu\) is called modulation factor

When \(\mu\) is expressed in percentage it is called modulation percentage.

The modulation factor expression is,

\(\mu =\frac{A_{max}-A_{min}}{A_{max}+A_{min}}\)

And the percentage modulation is,

\( \mu(\%) =\frac{A_{max}-A_{min}}{A_{max}+A_{min}}\times 100\%\)

Now we can change the modulation index or depth by changing the potentiometer knob connected to the modulating signal output and the carrier signal.

The following shows the Amax and Amin values of AM waveform generated with modulating signal is 1KHz with 1.5V amplitude and carrier signal is 100KHz with 3V amplitude.

Using the above equation, the modulation factor and modulation percentage are:

\(\mu =\frac{275mV-107mV}{275mV+107mV}=\frac{168mV}{382mV}=0.439\)

and, \( \mu(\%) =\mu \times 100 = 0.439\times100=43.9%\)

#### Video Demonstration of AM modulator

The following video demonstrates how the above AM modulator circuit works.

#### Conclusion

So in this way we have illustrated AM modulation method using two bipolar transistor BC107. Other general purpose bipolar transistors like 2N3904,2N2222 or BC547 may also be used. We showed how to use LC band pass filter at the output of the modulator to generate AM. There are several ways to recover the message signal from AM signal such as using AM Envelope Detector Circuit or using integrated chip(IC) such as AD633 Analog Multiplier IC for AM demodulation. Another popular method of AM demodulation is to use the MC1496 Balanced Modulator IC.