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Design >> Analog Design >> Deriving Gm of circuit
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Message started by blue111 on Jan 9^th, 2017, 12:15am

Title: Deriving Gm of circuit
Post by blue111 on Jan 9^th, 2017, 12:15am

For the following LC filter implementation,

I understand that this is a gyrator, but how to relate the two accuracy knobs (<7:0> and <2:0>) to the resonance frequency ?

Resonance frequency = 1/[sqrt(Leq*Cs)]
Leq = CL/(Gm1*Gm2)

In other words, how to derive equation for Gm2 in terms of the two accuracy knobs ?

Title: Re: Deriving Gm of circuit
Post by subtr on Jan 9^th, 2017, 2:17am

Your amplifier is a source degenerated amplifier. So the actual Gm is gm/(1+gm.Rs). Now the gm is a function of current, W/L of your transistor. I hope you have the handles. If you want to increase Gm, increase current or reduce the Rs. As you see both vary Gm in different fashion and have different effects. Increasing current would look easy, but it will affect your current source's bias margin reducing CMRR. Increasing current will reduce the gain. But varying Rs will not give you a great range, but will not affect your dc operating much as it carries incremental current.

Title: Re: Deriving Gm of circuit
Post by deba on Jan 9^th, 2017, 9:53pm

The Gm2 for the bottom transconductor is given by gm6/(1+gm6*Rs/2). Assuming that M6 and M5 are same. I have neglected gds and other contributions while deriving the expression. gm6 is a function of the bottom current source and Rs is the tunable resistance.

Title: Re: Deriving Gm of circuit
Post by blue111 on Jan 16^th, 2017, 3:43am

Hi,

1) I am not sure how you derive Gm2 without considering the impedance looking into the drain of M4 or M3. http://whites.sdsmt.edu/classes/ee320/notes/320Lecture32.pdf

2) Besides, I was told that the tail current is a coarse accuracy knob, while the degeneration resistance (Rs) is a fine accuracy knob.

Any insights ? Thanks!

Title: Re: Deriving Gm of circuit
Post by blue111 on Jun 24^th, 2017, 6:31am

@subtr :

Quote:

Increasing current would look easy, but it will affect your current source's bias margin reducing CMRR. Increasing current will reduce the gain. But varying Rs will not give you a great range, but will not affect your dc operating much as it carries incremental current.

Could you elaborate more on your statement above possibly with some other references, diagrams or equations ?

Title: Re: Deriving Gm of circuit
Post by blue111 on Sep 13^th, 2017, 12:53am

For transconductance value of CMOS inverter, is it normal to be very small value ?

Title: Re: Deriving Gm of circuit
Post by sheldon on Sep 14^th, 2017, 7:25pm

You should be able to turn the block into an oscillator, reverse the inputs
to generate positive feedback. Then run transient simulation and look at
the frequency of oscillation. You know the frequency and the value of C,
calculate Gm.

Title: Re: Deriving Gm of circuit
Post by Horror Vacui on Sep 21^st, 2017, 10:45am

gm is a small-signal parameter. It depends on your operation point. I have doubts whether the OP was set correctly.
If you have the DC transfer characteristic of the inverter, than you have the gm as well. gm is its derivative.
Sheldon's suggestion is also good, but oscillation is usually large signal. So you will get some kind of gm average of the "operation points" traveled through during oscillation.

Title: Re: Deriving Gm of circuit
Post by sheldon on Sep 22^nd, 2017, 3:33pm

In general, if the gm stage is capacitively loaded, then the input voltage
should be Output Voltage Excursion/ open loop gain at frequency. So,
the effectively signal levels for the input devices should be small.

In general, the gm of a gm-C filter stage has some method of fixing the
gm to a constant value across the operating range. If it isn't then there
is distortion, that is, the gm changing as a function of input signal level
causes limits the dynamic range of the stage. The function of the source
degeneration resistors in the original schematic is region where the gm
in constant.

Title: Re: Deriving Gm of circuit
Post by RickyTerzis on Sep 26^th, 2017, 10:31am

Hi...i am a new user here. As per my knowledge the gm is a function of current, W/L of your transistor. I hope you have the handles. If you want to increase Gm, increase current or reduce the Rs. As you see both vary Gm in different fashion and have different effects. Increasing current would look easy, but it will affect your current source's bias margin reducing CMRR. Increasing current will reduce the gain.

Title: Re: Deriving Gm of circuit
Post by blue111 on Sep 29^th, 2017, 3:44am

As shown in the screenshot below, G-parameter two-port model is suitable for the active inductor made up of voltage-voltage feedcback mechanism.

Please correct me if I am wrong.

I am planning to use G-parameter to measure the inductance value created using this gyrator circuit.

Title: Re: Deriving Gm of circuit
Post by blue111 on Jan 30^th, 2018, 7:25am

In ngspice, .OP gave me the following:

I am looking at it now. Does anyone have any comment ?

Quote:

Initial Transient Solution
--------------------------

Node Voltage
---- -------
x1.in 2.09899
vout 0
vdd 3.3
vss 0
vtest 0
gm2.in 1.8
xgm2.g3 2.14857
xgm2.1 3.3
gm2.out 2.09899
xgm2.2 3.3
xgm2.5 1.8
xgm2.4 0.649101
xgm2.6 0.649101
xgm2.8 0.649101
xgm2.9 0.649101
x1.out 1.8
v_ip_gm2#branch 0
v_ip_x1#branch 0
v.xgm2.v_ip3#branch 4e-05
v.xgm2.v_ip4#branch 4e-05
v.xgm2.v_ip5#branch 4e-05
v.xgm2.v_ip6#branch 4e-05
v.xgm2.vb#branch 0
vtest#branch 0
vs#branch 0.00280043
vd#branch -0.00280043

I am stucked at getting this active inductor https://github.com/promach/frequency_trap/tree/development working. Could anyone help ?

I will proceed to S11 parameter check afterwards if things still stucked.