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Design >> Analog Design >> Question on LC VCO O/P SWING
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Message started by raja.cedt on Jan 13^th, 2011, 5:05am

Title: Question on LC VCO O/P SWING
Post by raja.cedt on Jan 13^th, 2011, 5:05am

hello all,
i have some question on LC vco swing. My VCO architecture is pmos current source and nmos based -ve resistance. i know that swing is more or less Itail*Rp*2/pi. Here is the question.

while explaing swing people will say that during oscillations current swings from +I/2 to -I/2, out of this fundamental current component is flowing through effective R and hence 2*Itail*R/pi. But for maintaining oscillations total tank resistance and -ve resistance offered by active device are equal so effective tank parallel impedance is very high. But in swing equation Rp indicates only tank impedance,whats this discrepency.

Sorry to ask this but this gave me lot of confussion.

Thanks.
Rajasekhar.

Title: Re: Question on LC VCO O/P SWING
Post by vp1953 on Jan 13^th, 2011, 6:52pm

Hi Raja,

Here is my take - the resonator is modelled as a voltage source in series with a negative resistance; the lossy portion is modelled as a positive resistance. So the circuit looks like a voltage source in series with two resistors (both equal in magnitude but opposite in sign) both also in series- even though the net resistance is zero, the effective voltage across each resistor is I.Rp (their parallel resistance) and the voltage source having a magnitude of 2.I.Rp

Title: Re: Question on LC VCO O/P SWING
Post by raja.cedt on Jan 13^th, 2011, 10:25pm

hi vp1953,
sorry to ask you, i didn't understand why series model for resonator? Please clarify if you have time.

Thanks for your time.
RAJ.

Title: Re: Question on LC VCO O/P SWING
Post by ssahl on Jan 13^th, 2011, 11:14pm

Hi Raja!

The question is good and probably not simple to answer. I give it a try anyway.

Both way to see it is ok. The swing explaination only sees the cross coupled transitors as a bi-stable latch switching the current, nothing about a negative resistance in this case. Therefor the paralell resistance is only the one in the tank.

The alternative is to see the cross coupled pair as a negative resistance of -1/gm(V). Note that I say that gm is a function of the tank swing V. It has a maximum at V=0, which is 1/(Id/Vt) for a bipolar case. For larger magnitudes of V gm(V) reduces to zero. If 1/gm(0) < Rp then a oscillation builds up. When the amplitude increases the average gm will be reduces. At a specific amplitude the average of 1/gm(V) will be equal to Rp and the oscillation amplitude is defined.

If you manage to calculate the average of 1/gm(V) depending on the amplitude and set that equal to Rp you should get the amplitude of the oscillator. Hopefully that would be the same amplitude as the swing model. I tried to do the math for the bipolar case but I was stucked...

So, it is two ways to see the same problem.

Title: Re: Question on LC VCO O/P SWING
Post by vp1953 on Jan 14^th, 2011, 3:23pm

Hi Raja,

The small signal equivalent for the VCO is two resistors connected in parallel - one resistor is positive (loss) and the other is negative (resonator). In this loop of two resistors, there is a current I flowing to satisfy Kirchoff's voltage law and so the voltage across each resistor (voltage swing of the VCO)

is I.R
and (-I).(-R) [ the current has a negative sign because it flows in the opposite direction ]

You cannot use the combined resistance to calculate the voltage swing since there is no external current flowing into the loop.

Title: Re: Question on LC VCO O/P SWING
Post by raja.cedt on Jan 17^th, 2011, 1:16am

hello all,
now i understand understand clearly what is happening there. In large signal each -ve gm transistor carries !/2. where as in small signal current is switching from I/2 to -I/2 through tank. correct me if any thing wrong.

Last question on tank. I know that if resister added in series with inductor will reduce the frequency and resister in series with var-actor will increase the frequency. But if you consider tank inductor resistance and varactor resistance are in series so how come they behave differently from frequency point of view?

Thanks.

Title: Re: Question on LC VCO O/P SWING
Post by vp1953 on Jan 17^th, 2011, 3:01pm

Hi Raja,

Quote:

I know that if resister added in series with inductor will reduce the frequency and resister in series with var-actor will increase the frequency. But if you consider tank inductor resistance and varactor resistance are in series so how come they behave differently from frequency point of view?

The series circuit should be converted to its shunt equivalent and the L/C shunt equivalent is used for the resonant frequency calculation. For resistance in series with inductor, this increases the shunt inductance and hence frequency comes down. For resistance in series with capacitance, this decreases the shunt capacitance and hence frequency increases.