Transfer function for power mosfet and load

Hi,

I am trying to derive a transfer function for a system comprising of a power mosfet connected to a known load. Specifically, what I am looking for is H(s) = V_o(s) / V_gs(s) where H(s) is the overall transfer function (laplace transform of the system containing a power mosfet driving a load), V_o(s) is the laplace transform for the voltage across the load and V_gs(s) is the laplace transform of the gate voltage (or the control voltage) of the power mosfet.

We can assume that the load presents an impedance of Z_l(s) to the power mosfet whose source is connected to a constant source V_dd, drain is connected to the load impedance of Z_l(s) and gate is connected to the input of the system V_gs(s).

How do I go about deriving such H(s)?

I tried using the square law model of the mosfet in the saturation region but then it is non-linear so laplace transformations cannot be used. Can somebody explain step by step how to derive this?

Thanks,
NanoDim

By nature, linear transfer functions are only valid for small signal and a defined bias point (Vgs/Vds/Id). To derive a transfer function, you need to specify the bias point. Then you shouldn't have problems to determine the linear MOSFET parameters. You're apparently assuming a voltage source driving the FET, thus Cgs won't affect the transfer characteristic. Cds and Cgd should be considered together with the load impedance, however.

If the objective of your analysis is large signal behaviour, simply forget about Laplace and transfer functions. You need to proceed to non-linear differential equations instead.

FvM said:

By nature, linear transfer functions are only valid for small signal and a defined bias point (Vgs/Vds/Id). To derive a transfer function, you need to specify the bias point. Then you shouldn't have problems to determine the linear MOSFET parameters. You're apparently assuming a voltage source driving the FET, thus Cgs won't affect the transfer characteristic. Cds and Cgd should be considered together with the load impedance, however.

If the objective of your analysis is large signal behaviour, simply forget about Laplace and transfer functions. You need to proceed to non-linear differential equations instead.

Click to expand...

Thanks. Assuming I have one bias point for the power mosfet, then say I derive the required H(s) function. Now let us say I want to excite the system with a step response to determine how the system responds to a step change on its input. How can I be sure that the step change introduced will not violate my assumption for the small signal model for the power mosfet? Small signal model will be derived based on certain load current conditions, but this step change could be big enough to make the small signal model assumption in-accurate. Basically, what I am asking is that I if I assume a small signal model for the power mosfet, how can I find the limits of my step change such that the analysis would still hold for the given small signal model? Looking it in another way, how do we incorporate the change in the load current in the 'gm' change to keep the small signal model valid across all magnitudes of step changes?

Thanks,
NanoDim

By varying gm, the transfer function will become invalid anyway, because it's no longer a linear system. Either you can live with a certain degree of inaccuracy, or you should apply non-linear analysis, e.g. using a SPICE simulator. There's no inbetween.