# Help me understand this example- colpitts oscillator

#### Neyolight

Joined Dec 13, 2011
54
Hi all

I got the following example from a book

Example 3.10
Design the op-amp Pierce oscillator in Figure (attached) to oscillate at 10 kHz.

Ans:
The op amp used is a general-purpose op amp, such as the 1458 or 741. General-purpose op amps have typical slew rates of 0.5 V/ ￿ s and gain-bandwidth products(fT ) of 1 MHz. These parameters limit the frequency of oscillation. Of course,there are many special purpose op amps with high slew-rate values and high fT values, which can be used to attain higher frequency of oscillation.
Using supply voltage values of V+=5V and V −=−5V, the op amp output islimited to its saturation values (i.e., approximately±5V). In this case the
SR limitsthe frequency of oscillation to:

fo = SR/2*pi*Vo = (0.5*10^6) / 2*pi*5 = 15.9 kHz

MY QUESTION : I am designing a colpitt oscillator with LF351N which has the following features,
1) Slew rate = 16V/us
2) Gain Bandwidth product = f=100kHz
3) Using 9V DC supply

So going by above equation my frequency of oscillation

fo = 16*10^6/ 2*pi*9 = 282942.12 Hz =0.2 Mhz

Am I correct? Im just lost as to what to do next and even with this set ! How do I get started in building a colpitts oscillator?

Kindly help

#### t_n_k

Joined Mar 6, 2009
5,455
It's apparently based on the notion that the resulting output oscillations would be described by a function of the type

Vout=Vm*sin(ωo*t)

where

ωo=2*∏*fo

The value of Vm is limited by the op-amp being able to achieve maximum unbounded swing of up to the supply rail voltage at most. That's optimistic for many op-amps but probably close enough for the purpose of the exercise.

The maximum slew rate occurs when the sinusoidal signal output is at its maximum rate of change.

You find this corresponds to the maximum value of the derivative of Vout.

That occurs when max(d(Vout)/dt)=ωo*Vm=SR [max]

Hence this leads to the relationship

SR[max]=2*∏*fo[max]*Vm

Where Vm is half the amplifier rail-to-rail supply voltage. This gives the constraint for the maximum achievable operating frequency fo[max]

One could, in principle, electronically limit [say by feedback??] the op-amp sinusoidal output signal excursions to something less than the rail voltage limit value - thereby allowing a somewhat higher notional maximum operating frequency.

There should be any number of notes on the web on the Colpitts Oscillator design process.

Such as ...

http://www.electronics-tutorials.ws/oscillator/colpitts.html

or

http://hyperphysics.phy-astr.gsu.edu/hbase/electronic/posfe.html#c3

Last edited:
• Neyolight

#### Audioguru

Joined Dec 20, 2007
11,248
Your numbers for the LF351 opamp are very wrong. I am posting correct numbers from its datasheet.

I posted your oscillator circuit in your other thread (why two threads about the same oscillator?) from a tutorial I found in Google. Find it and it will tell you how to design the oscillator.

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• Neyolight