## Monday, July 14, 2014

### Design and Simulation of RC Phase Shift Oscillator in Matlab 2014

An RC Phase Shift Oscillator is used as audio oscillator and is an oscillator in simple form. An RC phase shift oscillator can use transistor or operational amplifier for its amplifier part. A BJT Transistor amplifier with RC feedback network is designed and stimulated in Matlab 2014 simscape/simelectronics.

In the earlier post the BJT transistor amplifier with RC feedback network was modeled in Simscape/ Simelectronics tools. The Oscillator model is again shown here,
The amplifier block contain is shown below,
and the content of the RC feedback subsystem is shown below,
What lies ahead is series of calculation for modelling the BJT transistor for use in the transistorized amplifier above. In matlab simelectronics the NPN transistor requires parameter inputs obtained from datasheet and many which are not available in the datasheet. For example the reverse current transfer ratio and problem of how to calculate collector and emitter resistance from the transistor datasheet.

In the BJT amplifier part we need to select the transistor and bias the transistor with appropriate value of resistors.

Using small signal modelling one can derive the requirement for a transistor to be used as an amplifier. The frequency for sustained oscillation in Hz is given by,
$f=\frac{1}{2\pi \sqrt{6}RC}$
From the above equation, selecting frequency of oscillator as 20KHz and using R=4.7Kohm we get the value of C as 0.6915uF

One can derive and show that one transistor property for using it as an amplifier for the RF phase shift oscillator circuit is the minimum value of forward current gain of the transistor and is given by,
$h_{fe}=44.5$

A transistor with forward current gain of more than 44.5 should work as the amplifier's transistor. We select the 2N3904 transistor. Once we select a transistor, we have to change the parameters of the NPN Transistor. The parameters required for the transistor is seen when it is double clicked.

Now we have to make appropriate changes so that the transistor behaves like the 2N3904 transistor. The parameters above can be obtained from the 2N3904 transistor datasheet. Part of the datasheet is shown below.

Here, the forward current gain is taken as 100. The output admittance can be found out from the output admittance graph available in the datasheet as shown below.

The output admittance from the graph is 60μmhos.

The collector current at hfe=100 is 10mA and collector-emitter voltage is 1V both obtained from the datasheet. The Vbe voltage is 0.65 and the Ib current can be calculated using the equation,
$\beta=h_{fe}=\frac{I_c}{I_b}$
which gives Ib=10mA

The reverse current transfer ratio,BR is the Ideal maximum reverse current gain. This value is not found in transistor datasheets as it is not important when the transistor is biased to operate in the normal active region. Since the transistor will not be operated on the inverse region, we can use the default value of 1.

Altogether the values in the window is shown below,

Next is the the Ohmic Resistance tab which allows to specify the collector, emitter and zero bias base resistances.

In the capacitance tab, we require the junction capacitance and the transit time which are as follows,

This completes the frequency, R and C values and the transistor setting.

Next the biasing resistor values have to be calculated which will be done in the next blog post.

See the earlier posts on oscillator-
Oscillators in communication system
Condition of producing Oscillation from oscillators
How RC Phase Shift Oscillator Works?