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A question about Microwave Oscillator.

A question about Microwave Oscillator.

A question about Microwave Oscillator.

Many Microwave textbooks told me that during the process of oscillation, initially, it is necessary for the overall circuit to be unstable at a certain frequency, that is the loop resistance should be negtive.

but I find this theory incorrect, when I try these values:

Zload=75+j*30; (load impedence)
Zin=-100-30*j; (impedence looking into the negtive resistance device)
Z0=50; (characteristic impedence)
I found
Rloop=-100+70=-30<0   but
abs(GamaLoad*GamaIn)=abs(((Zload-Z0)/(Zload+Z0))*((Zin-Z0)/(Zin+Z0)))=0.8 <1, so it is still stable!

what is wrong? is the theory wrong, or am I wrong?

Who can help me? Thanks!

RE: A question about Microwave Oscillator.

First, there is no "abs" in the equation.

Second, you probably have a math error.  If you are measuring with a 50 ohm network analyser, and your active device (the load) has an impedance of ZL= -100 -30j

Then p = (-100 -30j -50)/(-100 -30j +50)
= [(-150 -30j)/(-50 -30j)]
= [(-150 -30j)/(-50 -30j)] * [(-50 +30j)/(-50 +30j)]
= (9400 -3000j)/3400 = 2.47 -0.882j  which obviously is greater than unity reflection coefficient.

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