Greetings,

I am an undergrad student of electrical enginering and I am designing a colpitts oscillator. For a starting point I used a schematic in the following link:
http://www.learnabout-electronics.org/Oscillators/osc24.php
The requirement for my design was that the circuit oscillates at the frequency 30-40 kHz(inductor L1 in my design is variable,so frequency varies).
I made the following adjustments:
values of C1 and C4 large(I used 47 uF and 10 uF, since C1 and C4 represent short circuit at the operating frequency)
value of C2 is 220 nF
value of C3 is 100 nF
value of L1 is 300 uH +- 10 uH
Other elements in the circuit stayed the same.The circuit now oscillates at the desired frequency.

Now my question:What is the theory behind choosing the values of biasing resistor R1 and R2 for the given topology?

Thank you for your help!

 

What is the theory behind choosing the values of biasing resistor R1 and R2 for the given topology?

Generally, R1 & R2 form a Thevenin Equivalent bias network to set the current flowing through the emitter resistor R3. Or is the question rather how to decide what the current flowing through R3 should be? How much power can the transistor safely dissipate?

 

Or is the question rather how to decide what the current flowing through R3 should be?

Yes, this is my question.

 

I suspect that the bias point of the transistor is somewhat arbitrary, but you could verify that experimentally. Replace R1 & R2 with a potentiometer & base resistor to vary the bias current and note the effect on the oscillation. (Don't exceed the power rating of the transistor!) Then analyze the circuit in the complex frequency domain using an h-parameter model for the transistor, apply the Barkhausen Criterion, and see if that can explain the experimental results. When you finish with that you'll know a lot more about a Colpitts oscillator than I do.

 

Hi,

For a frequency of 40kHz you could most likely use a low frequency model of the transistor. Either a voltage controlled current source or a current controlled current source with some input resistance.

The question of bias point probably plays in with the gain of the transistor. As we vary the DC input current the gain of the transistor will change somewhat. The gain of the transistor will probably affect the distortion of the output such that it is either a fairly clean sine or a very clipped sine. Of course you cant bias it too much either or the current in the output will be too high and the transistor overall output impedance could make it harder for oscillation to occur due to the parasitic elements of the parts being used (such as inductor ESR).

There are other configurations you could look at too. Note that the DC voltage readings on the base and emitter of that circuit are not correct. We can not have 2.3v on the base and 2.2v on the emitter because the base emitter drop will be closer to 0.6 to 0.7 volts. Thus a reading of 2.2v on the emitter would result in a voltage of about 2.9v on the base.

 

I suspect that the bias point of the transistor is somewhat arbitrary, but you could verify that experimentally. Replace R1 & R2 with a potentiometer & base resistor to vary the bias current and note the effect on the oscillation. (Don't exceed the power rating of the transistor!)

This is a great experimental method for determining optimal values for biasing resistors. Will definitely try it as soon as i get access to the equipment again.

 

For a frequency of 40kHz you could most likely use a low frequency model of the transistor. Either a voltage controlled current source or a current controlled current source with some input resistance.

I will post the analysis in the next post.

 

I also have some questions about frequency analysis. While you read, please check and correct me if necessary.Here is is:

This is the circuit schematic:


for dynamic analysis, we can redraw it as:


Here is the block diagram of an oscillator:

 

Continuing post #8:

From the dynamic analysis schematic ,we identify the amplifier(open system ) and feedback.
Here is the open system:



Open system transfer function:

 

Continuing post #9:

Here is feedback:


feedback coefficient:
beta=C3/(C2+C3)

Calculating open loop gain:


Barkhausen criterion states:

T(jw)=1

or

1.|T(jw)|=1

2.<T(jw)=0

from the first condition we can calculate rbe.The second condition seems impossible for this system. Does anyone know how to explain that?Shouldn't both conditions be satisfied for the oscillation to start?

 

I also have some questions about frequency analysis. While you read, please check and correct me if necessary.Here is is:

This is the circuit schematic:
View attachment 131519

for dynamic analysis, we can redraw it as:
View attachment 131517

Here is the block diagram of an oscillator:

View attachment 131518

Hi,

Why are you putting a voltage source Vi in parallel to R3 in your second drawing there?
That effectively prevents any feedback from affecting the system right?

Here is a rough analysis using just one particular value for Beta.
The oscillations are increasing which means the transistor must start to clip at some point and that limits the output voltage level.
This response is in the time domain and comes about by turning the power supply from 'off' to 'on' fully with no previous energy stored in any circuit elements.
This result should be viewed as an example with a particular fixed Beta for the transistor not as the complete solution. Obviously something eventually clips the output so it cant go to infinity.

 

This result should be viewed as an example with a particular fixed Beta for the transistor not as the complete solution.

Having read various descriptions of the Colpitts oscillator, it seems clear that there are many different circuit configurations; however, they all share a resonant tank with a capacitor voltage divider providing feedback. Some configurations are described in terms of non-linear transistor operation briefly pulsing the current into the tank periodically to keep it energized. Not sure if that is the case for this particular Colpitts circuit. In your simulation does the transistor current show any pulsing indicative of non-linear operation, or is the current sinusoidal indicating more linear operation (and susceptible to linear analysis)?

 

Having read various descriptions of the Colpitts oscillator, it seems clear that there are many different circuit configurations; however, they all share a resonant tank with a capacitor voltage divider providing feedback. Some configurations are described in terms of non-linear transistor operation briefly pulsing the current into the tank periodically to keep it energized. Not sure if that is the case for this particular Colpitts circuit. In your simulation does the transistor current show any pulsing indicative of non-linear operation, or is the current sinusoidal indicating more linear operation (and susceptible to linear analysis)?

Hi there,

Well first it's not a simulation, it's a straight up calculation using Nodal Analysis. I supposed we should do a simulation too but the OP should be doing that. Most people dont like getting into the nitty gritty calculations for more complex circuits, so i sometimes do that to be able to contribute a little more information on the topic circuit(s).

The calculations show that the response is sinusoidal with a damped exponential part as well as an undamped exponential part. After a very very short time the damped exponential runs it's course and so is no longer affecting the response, so the sine continues, but the undamped exponential factor causes the sine to continually increase, and that would be common in an oscillator. The idea is to make the gain slighty more than needed and then use some non linear way to limit the gain in order to maintain a nearly constant output with low distortion.

What you see there is actually a linear analysis, and i leave the non linear part out of it because that would not kick in until the wave form builds to some amplitude. After that, some non linear clipping would limit the output. How bad that would be would have to be investigated. We would hope for a sine wave, and perhaps adjust the input bias for best distortion. Note that if the output tries to go too negative the collector base diode would start clipping. Would be interesting to do a simulation too though.

 

Now my question:What is the theory behind choosing the values of biasing resistor R1 and R2 for the given topology?

Thank you for your help!

Do you want to know just about R1 and R2?
It is polarization of the transistor in DC.

How does this oscillator work?


L1, C2 and C3 it is a oscillating circuit LC parallel.



From
https://en.wikipedia.org/wiki/LC_circuit
Where L=L1 and 1/C=1/C2+1/C3 (series grouping C2 and C3)

This is the frequency of oscillation just in the first approximation.
Frequency of oscillation depends evenly on R1 and R2.
The transistor has parasitic capacities and parameters at high frequency.

The transistor works the common base.
C1 is large enough for the base to be connected at the "GND" for the work frequency.

With base at "GND"(actually at the fixed electrical voltage on R2), the command signal receives it in the emitter via C4(feedback).


C4 is chosen so that the oscillations are starts. (The condition that the circuit to start oscillating)
C4 also achieves the phase shift -oscillation condition

From
http://www.electronicshub.org/oscillator-basics/

If you want we can continue the calculation........
So, as shown in the figure I needed an amplifier. R1 and R2 for polarization of the transistor are calculated as a simple single transistor amplifier.