AM or Amplitude modulation is one of several method of modulation in which the information signal or the modulating signal amplitude is used to vary the carrier signal. The frequency of modulating signal or the message signal is much less than then the carrier signal(also called local oscillator signal). In this way a signal of low frequency can be transmitted using high frequency carrier signal because due to modulation, the carrier signal carries the information signal with it. AM modulator circuit can be constructed using discrete diode and transistor components. Some of AM modulator design were explained in the previous tutorials Single Diode Modulator, Double Balanced Diode Ring Mixer design, mixer or modulator circuit using BJT transistor. Here a AM modulator circuit using JFET transistor is illustrated.
The circuit diagram of JFET transistor based simple AM modulator is shown below.
We have used here N-channel 2N3819 JFET transistor. The JFET is biased using self biasing method(see How to bias JFET transistor?). The modulating signal(vm) is applied to the gate of the JFET transistor via the coupling capacitor C3. The carrier signal(vc) is applied to the modulator via the coupling capacitor C4 on the source of the JFET transistor. An LC resonant tank which is resonant at the carrier signal frequency is connected to the drain. The output is taken from the drain to the load resistor RL via the coupling capacitor C2.
The modulating signal with frequency \(w_{m}=2 \pi f_{m} t\) and amplitude \(V_{m}\) can be written as,
\( v_{m} = V_{m} Sin(2 \pi f_{m} t) = V_{m} Sin(w_{m} t) \)
The modulating signal waveform is illustrated below.
Similarly, the carrier signal or local oscillator signal can be expressed as a sine wave of frequency \(w_{c}=2 \pi f_{c} t\) and amplitude \(V_{c}\),
\( v_{c} = V_{c} Sin(2 \pi f_{c} t) = V_{c} Sin(w_{c} t)\)
When the modulating signal modulates the carrier signal the envelope of the resulting AM signal is modulating signal and the carrier signal is the underlying varying waveform as shown below.
As can be seen from the above diagram, the modulating signal waveform varies below and above the carrier signal amplitude 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,
\[ V_{c} > V_{m} \]
The standard equation for the AM signal is derived by the fact that the modulating signal reference point is the peak value of the carrier signal amplitude. It means that the instantaneous modulating signal is added or subtracted from the peak value of carrier amplitude. Thus the amplitude of the AM signal is the sum or difference between the carrier amplitude and modulating signal. That is mathematically, the amplitude of AM signal is,
\[ V_{am} = V_{c}+ v_{m} = V_{c}+ V_{m} Sin(w_{m} t) \]
Thus the mathematical expression for AM signal is,
\[ v_{am} = V_{am} Sin(w_{c} t) = (V_{c}+ V_{m} Sin(w_{m} t)) Sin(w_{c} t) \]
Let us use the ratio of the modulating signal amplitude to carrier signal amplitude called the modulation index m,
\[m= \frac{V_m}{V_c}\]
Then we can write the equation for AM signal as,
\[ v_{am} = V_{c}(1+ m Sin(w_{m} t)) Sin(w_{c} t) \]
In the above JFET AM modulator circuit, if the modulating signal amplitude is 100mV and frequency is 1KHz and if the carrier signal amplitude is 500mV and frequency is 10KHz then the modulation index has the value of 100mV/500mV= 0.2. This expressed in percentage is 20% called percentage of modulation.
We can expand the above AM signal equation as follows,
\[ v_{am} = V_{c} Sin(w_{c} t) + m V_{c} Sin(w_{m} t) Sin(w_{c} t) \]
or,
\[ v_{am} = V_{c} Sin(w_{c} t) + \frac{m V_{c}}{2} (Cos(w_{m}+w_{c}) t) + Cos(w_{c}-w_{m}) t)) \]
In the above equation, the first term is the carrier signal, second and third terms is what causes characteristics of AM signal.
The following is frequency spectrum of the AM signal of the above JFET modulator which shows the carrier signal at 10KHz and the sum and difference spectra at 9KHz and 11KHz along with intermodulation products.
The following shows modulating signal, carrier signal and AM signal waveform on oscilloscope.
As can be seen in the above oscilloscope, the amplitude of the AM signal is very low. The output AM signal has to be amplified in further stages when designing AM transmitter.
Furthermore, the amplitude of the message signal used here is 100mV while the carrier signal amplitude is 500mV. When the message signal amplitude gets higher than the carrier signal amplitude then overmodulation condition results. When overmodulation happens, the message information is lost and cannot be recovered during demodulation at the receiver. This type of error or distortion is called overmodulation distortion. The following video shows animation of how overmodulation happens.
See next how to design AM modulator using BJT Transistor.
