You change the resistance by changing Vgs. For low resistances, the resistance would not be a function of current, except to for the nonlinearity of the FET (there will always be some nonlinearity, even in the "linear" region).
You can use a FET as a VCR, but each unit will require a different Vgs to get a given value of resistance, so it would not be suitable for production.
Some people use JFETs in this application, but they are generally in a feedback loop, where the resistance value is servoed to accomplish a function such as automatic level vontrol.
JFETs are small-geometry devices, so their resistance is higher, which I think might be better for your application. If you use a switching MOSFET such as IRF3703, I think your resistance will be extremely nonlinear if you try to attain resistances on the order of thousands of ohms. If you are looking for milliohms, you should be OK with the power MOSFETs.

Ok, i get the nonlinearity idea. The low resistances you mean here is referring to miliohms range, which is the Rds(on) value shown in specification right? Per my understanding, the Rds(on) is occurring in saturation region. Is the my previous simulated resistance which is in kΩ range or the IRF3703 resistances on the order of thousands of ohms as you have mentioned operating in linear region? When we are biasing the MOSFET at different Vgs AND without Vds biasing, are we operating the MOSFET in linear region (left region of dash line) as shown in IV Curve.png? Please be patient with my simple questions as I am trying to make myself clear

 

If you Google "voltage-controlled resistor", you will find information about JFETs and other techniques.
VCR2N4N7N is a JFET which is specifically designed to be used as a VCR.

Have you searched for "voltage controlled filter"? You might find something useful.
Here is an example:
http://www.musicfromouterspace.com/analogsynth/AAA_VCFilterIndex.php

Don't stop there. Be creative in your searches.

Thanks. Yes, I have been searching all around, even technical papers in IEEE, but most of them are being implemented within the chip level. What I am trying to do is off-chip, as I don't have the chip fabrication facility. The information are useful, I will study on them. Anyway, off-chip work are more fun for me

 

When you run the MOSFET without bias, current can flow in both directions when you use it as a resistor, but will only do so if you apply a signal which is both positive and negative. Below is what the curves look like if you do this.

EDIT: This transistor's Rds=4mΩ. If you simulate it a low values of Vgs, the resistance goes up, but, as I stated previously, it gets very nonlinear, and probably unstable vs temperature and small changes in Vgs.

 

When you run the MOSFET without bias, current can flow in both directions when you use it as a resistor, but will only do so if you apply a signal which is both positive and negative. Below is what the curves look like if you do this.

EDIT: This transistor's Rds=4mΩ. If you simulate it a low values of Vgs, the resistance goes up, but, as I stated previously, it gets very nonlinear, and probably unstable vs temperature and small changes in Vgs.

Thanks for the simulation, now I can see a clearer picture. So the switching MOSFET did provide a very low resistance at linear region. Looking back what you have mentioned:

If you use a switching MOSFET such as IRF3703, I think your resistance will be extremely nonlinear if you try to attain resistances on the order of thousands of ohms

To obtain a thousand ohms of resistance, I will need to bias a very high Vds value right? In saturation region, as I increase the Vds, the drain current would still maintain the same, hence the resistance at the channel increase, according to ohm's law. Please correct me if I am wrong.

Previously I obtained kΩ range resistance in my Multisim simulation, why was that happened? Is it because the ohmmeter provide a very high voltage across the drain-source terminals during measurement?

 

Thanks for the simulation, now I can see a clearer picture. So the switching MOSFET did provide a very low resistance at linear region. Looking back what you have mentioned:



To obtain a thousand ohms of resistance, I will need to bias a very high Vds value right? In saturation region, as I increase the Vds, the drain current would still maintain the same, hence the resistance at the channel increase, according to ohm's law. Please correct me if I am wrong.

When using a FET as a VCR, I think that you should generally be operating it in the linear region, near 0 volts and 0 current. Otherwise, it will be nonlinear. I suppose you could bias it into the saturation region, but this would be pretty tricky for filtering a signal with a DC component such as in a PLL loop filter.
I think a JFET would be more appropriate for discrete circuits. Are you trying to figure out how to include this in a CMOS IC, which doesn't have JFETs available? Small-geometry MOSFETs, such as in an IC, will generally have Rds(on) on the order of thousands of ohms. Small geometry discrete MOSFETs are uncommon. You might find a DMOS device that could work for you.

Previously I obtained kΩ range resistance in my Multisim simulation, why was that happened? Is it because the ohmmeter provide a very high voltage across the drain-source terminals during measurement?

Weren't you using a generic spice model when you got those results?

 

When using a FET as a VCR, I think that you should generally be operating it in the linear region, near 0 volts and 0 current. Otherwise, it will be nonlinear. I suppose you could bias it into the saturation region, but this would be pretty tricky for filtering a signal with a DC component such as in a PLL loop filter.
I think a JFET would be more appropriate for discrete circuits. Are you trying to figure out how to include this in a CMOS IC, which doesn't have JFETs available? Small-geometry MOSFETs, such as in an IC, will generally have Rds(on) on the order of thousands of ohms. Small geometry discrete MOSFETs are uncommon. You might find a DMOS device that could work for you.

Yes, I will study about JFET soon, thanks for the suggestion. No, I am not trying to figure out how to include it in an IC, I am working on off-chip stuff. I was just wondering how they can get high resistances using MOSFET. Ok, I got your point of high Rds(on) in a small scale transistor such as in an IC.

Weren't you using a generic spice model when you got those results?

Yes, I used generic model. The attach shows the info when I double click the MOSFET. The channel length and width are 100μm. Do you think this length and width values give kΩ range resistance?

 

Yes, I used generic model. The attach shows the info when I double click the MOSFET. The channel length and width are 100μm. Do you think this length and width values give kΩ range resistance?

Go back to your books. Channel resistance is proportional to L/W. With an L/W=1, I'm not surprised that you got kΩs of resistance.

 

Go back to your books. Channel resistance is proportional to L/W. With an L/W=1, I'm not surprised that you got kΩs of resistance.

The formula is,

R(on) = 1 / μnCox(W/L)(Vgs-Vth)

If I assume μnCox is 50μA/V^{2}, then the resistance is in kΩ range. The modeling of the MOSFET in my simulator is as below:

+ (
+ LEVEL= 1
+ VTO= 0.0
+ KP= 2.0e-5
+ GAMMA= 0.0
+ PHI= 0.6
+ LAMBDA= 0.0
+ RS= 0.0
+ RD= 0.0
+ CBD= 0.0
+ CBS= 0.0
+ IS= 1.0e-14
+ PB= 0.8
+ CGSO= 0.0
+ CGDO= 0.0
+ CGBO= 0.0
+ RSH= 0.0
+ CJ= 0.0
+ MJ= 0.5
+ CJSW= 0.0
+ MJSW= 0.5
+ JS= 0.0
+ TOX= 1.0e-7
+ TPG= 1.0
+ LD= 0.0
+ UO= 600.0
+ KF= 0.0
+ AF= 1.0
+ FC= 0.5
+ TNOM= 27
+ )

I am just wondering which is μnCox or how do I calculate μnCox from these values? Any idea?

 

I'm assuming you know that μn and Cox are two different parameters. Cox is process-dependent. It is a function of gate oxide dielectric constant (which is usually, or maybe always, SiO2, not sure) and thickness. μn is the charge-carrier effective mobility. I don't know if it is a constant, or is process-dependent.