Discussion in 'Homework Help' started by anhnha, Oct 15, 2013.

1. anhnha Thread Starter Active Member

Apr 19, 2012
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For example, there is a circuit as in the picture. I removed coupling capacitor and arrange it as below to make it simple, though I know it is only in theory not practical.

VGS: Bias voltage to make M operate in saturation region.
vgs: Small signal voltage that need to be amplified.
Let's assume that VGS= constant so that the transistor is in saturation region.
And the small signal:

$v_{gs} = V_{0} sin( \omega t)$

The transconductance of the transistor, gm, is:

$g_{m} = \mu _{n} c_{ox} \frac{W}{L}( V_{GS} - V_{TH} ) = constant$

Drain current, iD:

$i_{D}= g_{m} v_{gs}= g_{m} V_{0}sin( \omega t)$

The voltage across the inductor:

$v_{L} = L \frac{d i_{L} }{dt} = L \frac{d}{dt} (g_{m} V_{0}sin( \omega t)) = \omega Lg_{m} V_{0}cos( \omega t)$

The voltage at D:

$v_{D}= -v_{L} + V_{DD} = - \omega Lg_{m} V_{0}cos( \omega t) + V_{DD}$

If gm, ω, VGS are fixed, then the magnitude of vL is directly proportional with L. We can make it lager arbitrarily by choosing the value of L.
And therefore, the voltage swing at D can be very large beyond the range from 0 to 2VDD, right?

I have heard somewhere that the maximum voltage swing at D is 2VDD and ranges from 0 to 2VDD.
Is that right?

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2. Efron Member

Oct 10, 2010
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If you make the DC analysis of the circuit, the voltage at D at operating point is VDD (L behaves as shortcut).

Meaning that, if ever oscillations are possible, these will be done from this operating voltage VDD. Assuming that the MOSFET can swing from one extreme to the other, the output voltage will be from 0 to 2*VDD (ac oscillation of VDD volts amplitude).

3. Efron Member

Oct 10, 2010
81
15
Are you sure of the sign of this formula? shouldn't the relationship between VL and IL be negative.

4. anhnha Thread Starter Active Member

Apr 19, 2012
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In DC mode, VD(dc) = VDD
In AC mode, VD(ac)= -gm*(ωL)*vgs
=> The voltage at drain of the transistor:
VD = VD(dc) + VD(ac)= VDD - gm*(ωL)*vgs
For example, vgs = Vo*sin(ωt).
VD = VDD - gm*(ωL)*Vo*sin(ωt)
Huh, a bit different with the one I made above. Maybe, I mistake somewhere.

My confusion is why you know that 0 < gm*(ωL)*Vo < VDD ?

Apr 19, 2012
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6. Jony130 AAC Fanatic!

Feb 17, 2009
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I also never heard about "open channel condition".
But I suspect that Id_max = Vdd/Rd = open channel condition.

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7. anhnha Thread Starter Active Member

Apr 19, 2012
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Thanks Jony. That seems right. However, I wonder why the characteristic Vgs-Ids depends on its load, Rd.
And can you explain about maximum voltage swing at D is 2VDD?

Apr 19, 2012
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9. Jony130 AAC Fanatic!

Feb 17, 2009
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For the inductive load, the DC voltage at drain is equal to Vdd. And so the maximum negative voltage swing is from VDD to 0V.
And so in order to keep the waveform symmetrical we "limit" the positive voltage swing to 2VDD (swing from Vdd to 2Vdd).

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10. anhnha Thread Starter Active Member

Apr 19, 2012
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In other cases, for example, in AB or C class power amplifiers, there is a filter at output. And therefore, we don't need to keep the voltage at drain symmetrical.

Is that right?

Can you help me derive that formula below in the part of my book above?

$P_{OUT} = \frac{ V_{DD}^{2} }{2 R_{OPT} }$

11. Jony130 AAC Fanatic!

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I don't know

the average power is equal to

P = Vrms * Irms = Vrms^2/R

But if we use Vpeak instead of Vrms we have this situation

P = Vrms^2/R = [ (Vp/√2)*(Vp/√2) ]/R = (Vp²/2)/R = Vp²/2R

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12. anhnha Thread Starter Active Member

Apr 19, 2012
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Well, I got stuck at that for two days. I know the formula but didn't think about it.

I don't know why this optimum resistance provides the best linearity to the PA. To me it provides maximum voltage swing not linearity.
And in the figure drain current and drain voltage not reach their maximum values at the same time. As VDS max IDS = 0 and vice versa. Can you tell me what the book meant here?

Last edited: Oct 17, 2013
13. Jony130 AAC Fanatic!

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It seems that they assume that ID_max = IDmax for a given MOSFET and use idealized VDS–IDS model. So in this case Ropt provides in the same time the best linearity and max power at load.

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14. anhnha Thread Starter Active Member

Apr 19, 2012
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For MOSFET, the power dissipation in transistor:
P = Vds*Ids and we always want this as low as possible, right?

15. Jony130 AAC Fanatic!

Feb 17, 2009
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Yes
Yes, but in some circuit we have to deal with it. For example in class A amp
P = Id_Q * Vds_Q
Q = quiescent point

And this power dissipation is independent of a active device we choose to use in the amplifier.

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