# k factor for rf amps and oscillators

#### capybara

##### Senior member
please define the k factor. i mean the one which (best as i can remember) if k > 1
an rf ckt amplifies, if k<1 the ckt oscillates (rings). K= what ???
and define all the un-obvious terms
<<<besides f=frequency, c=capacitance , l=inductance,
x sub c = capacitive reactance, x sub l = inductive reactance, r =resistance>>>
sorry for the stupid question, but room-mates threw out my EE books!

#### jteef

##### Golden Member
I dont know if this will help you or not. If you're talking about the rollett stability factor then in terms of S-parameters:

kr = (1-|S11|^2 - |S22|^2 + |Ds|^2) / ( 2*|S12| * |S21| ) >1

where Ds = S11 * S22 - S12 * S21

|S11| & |S22| should also be less than 1

also |S12*S21| <1 - |S11|^2

and

|S12*S21| < 1 - |S22|^2

also need to be satisfied for inherent stability

If you dont know S-parameters, you should learn them. there are probably some pages/tools on the web to get you started in the conversion process.

jt

#### highwire

##### Senior member
capybara -

K as you decribe is LOOP GAIN.

If you have an amplifier with a gain of 100 and feed 1/100 of the output back to the input , the loop gain is 1, the product .

The game in amplifier design is to have a loop gain of less than 1 at all frequencies for stable operation. S params will help get you there in style. Well, in an orderly fashion, anyway.

#### capybara

##### Senior member
umm....my problem with S-parameters is that they are measurements after a system is built.
im looking for the k factor or parameter that is a calculation which can be made before a system is built
K=f(frequency, L input, c input, L output, c output)
I saw it in the book Electricity 1-4 or Electronics 1-4.