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Can inductance in the gate circuit cause a negative resistance at the source terminal

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Fractional-N

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negative resistance

89_1219218716.jpg

image from the design of cmos rf integrated circuits-2nd ed (Cambridge, Lee, 2004) page 642

inductance in the gate circuit of a common-gate device can cause a negative resistance to appear at the source terminal

how you prove that? (how you show that?)
 

negative resistance

Theorotical:
Convert S parameter in to Z parameters.
Add XL that is inductance to Z parameters
Again convert to S parameters.
If your S11 is >1 means you have obtained negative resistance.
You find the details about the explanations in following books
You can tally this using S11 equation. (zin-zo/zin+zo)
1) Microwave transistor amplifiers by gonzalez
2) microwave devices & circuits by Lio PHI publication

If you want to see this practically
Use simulators such as ADS
there you can directly check using tools
 

    Fractional-N

    Fractional-N

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Re: negative resistance

Here is an attempt for an obvious and evident explanation of the effect:

A negative resistance can be thought of a voltage controlled current source which drives a current back into the voltage source.
In the circuit shown this can happen when a voltage at the source pin drives a current into the FET which causes a small current through the GS capacitance and the inductance between gate and ground (for rather high frequencies).
As a result, a voltage is created across the inductance which in turn causes a drain current (normal FET operation) which goes into the voltage source at the source pin. Thus, for a certain frequency range this circuit has a negative input resistance at the source pin.
 

    Fractional-N

    Fractional-N

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negative resistance

Or you can consider this structure as a three port device. When you calculate 3 port s-parameters by adding a reflection coefficient at third port ( see Solid State Radio Design-I.Bahl, Prakesh et al.) you'll see S11>1 that is equivalent to negative impedance..
 

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