Oscillators circuit analysis

1. Oscillators circuit analysis Identifying the open loop gain is a useful technique for oscillator analysis However there are circuits where it is difficult to apply the open loop gain For this reason two additional methods of oscillator design and analysis will be presented These two methods are The direct analysis of the circuit equation The negative resistance concept 1

2. Circuit analysis The three terminal device could be either a BJT or FET transistor The three external impedances represent feedback connections 2

3. Circuit analysis The small signal equivalent circuit is given below 3

4. Circuit analysis The loop equations for the small signal circuit are Note that the voltage v can be determined from the equation below This equation can be rearranged as 4

5. Circuit analysis The above two equations in matrix form can be rewritten as For the circuit to oscillate the determinant of the coefficient matrix must be zero, that is 5

6. Circuit analysis The above equation can be rearranged as shown below For simplicity only the case when Zi is real value will be considered (i.e. ) The previous equation can be rewritten as 6

7. Circuit analysis The last equation can be satisfied if Since rπis a positive number, then Or This results shows that Z1 and Z2 must have the same impedance type (ie if Z1 is a capacitor, then Z2 is a capacitor too and Z3must be an inductor) 7