## Sunday, July 13, 2014

### Oscillators in Communication System

Oscillator are essential components in communication system. Oscillator generates an output signal with constant amplitude and constant frequency without any input signal. They are used to produce carrier signal onto which message signal are embedded and transmitted over the air to the destination receiver. They are required in all communication system such as AM modulation and circuits, FM and in digital communication system.

Below is a block diagram of a typical transmitter and receiver in which the function of oscillator is illustrated.

In the block diagram the oscillator produces the carrier signal of desired frequency. This carrier signal is mixed with the message signal in the modulator. The modulated signal is sent to the power amplifier which amplifies the signal to the desired power level and gets transmitted over the air the receiver via the antenna.

The basis and principle of oscillator is an amplifier connected with a feedback block. The amplifier can be a non inverting and inverting type. In the non inverting type amplifier, the signal is fed to the positive terminal of the opamp and in inverting opamp the signal is connected to the negative terminal of the opamp. A non-inverting opamp has output that is in phase with the input while an inverting opamp produces ouput signal that is 180 out of phase with the input signal.

A non-inverting opamp requires a positive feedback.  A feedback is said to be a positive one if the phase of its output signal is in the same phase(in phase) with the input signal.

In the above picture the Operational Amplifier and the Feedback Network are the parts of the oscillator. If the amplifier is non inverting then the phase of input and output signal of the amplifier are in phase. The positive feedback provides no phase change and therefore the phase of the input signal of the amplifier and the output of the feedback network are also in phase.

The positive feeedback network feed backs some fraction of output signal Vo back to the input of the amplifier. This is called feedback gain beta and is defined as follows,
$\beta= \frac{V_f}{V_o}$     -----(1)

The open loop gain 'A' is defined as the ratio of Vo to Vin,
$A= \frac{V_o}{V_{in}}$            -----(2)
The overall gain for the circuit, is called the closed loop gain or the gain with feedback and is given by-
$A_f= \frac{V_o}{V_s}$       -----(3)
The signals Vs, Vin and Vo are related by the equation-
$V_{in}=V_s+V_f$    ------(4)
using (1) Vf is,
$V_f=\beta V_o$     ------(5)
Using (5) in (4) we get,
$V_{in}=V_s+\beta V_o$
or, $V_s=V_{in}-\beta V_o$    ----(6)
using (6) in (3) we get,
$A_f= \frac{V_0}{V_{in}-\beta V_o}$   ----(7)
Dividing RHS of (7) by Vin and using (2) we get relation between Af and A as follows,
$A_f= \frac{A}{1-\beta A}$

This is a relation between the closed loop gain and open loop gain.