Input Resistance of Common Gate question....

In summary, the input resistance of a common gate amplifier goes to 1/gm as ro goes to infinity. When you calculate the input resistance of a voltage amplifier you need to assume the output is connected to a high impedance. So your third current (that you set to zero) is wrong. The KCL equation should be ix = gmvx - vx/ro - (vx-vo)/ro So the KCL equation should be ix = gmvx - vx/ro - (vx-vo)/ro
  • #1
perplexabot
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Hey all. I have been trying to calculate the input resistance of a common gate amplifier, but seem to have problems doing so.

I know I have to set a test voltage (or test current) at the input, and I've been told, to ground the output. So using the Hybrid pi model for a mosfet, I did the following to calculate the input resistance:
Untitled.png


I apologize for my low quality picture. Please any help or hints are greatly appreciated. I just don't know what I am doing wrong. I have used the exact same technique on other amps and it seems to have worked fine, just not with common gates amps : (

Thank you.
 
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  • #2
What's the problem? You got the right answer. The input resistance of a common-gate amplifier goes to 1/gm as ro goes to infinity.

If you're trying to calculate it including Rd (which is not standard but sometimes done) then you forgot to include the current going from the VCCS to ground through Rd (equals Vo/Rd).
 
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  • #3
analogdesign said:
What's the problem? You got the right answer. The input resistance of a common-gate amplifier goes to 1/gm as ro goes to infinity.

If you're trying to calculate it including Rd (which is not standard but sometimes done) then you forgot to include the current going from the VCCS to ground through Rd (equals Vo/Rd).

Thank you for your time and reply. Yes, I am trying to include Rd. If I take the node above the test voltage, there are 3 currents going in and out of that node. Rd doesn't seem to be part of any of those three. It also seems that Rd is shorted out due to connecting Vo to ground. How does one incorporate Rd into the equation?

Once again thank you so much.
 
  • #4
perplexabot said:
Thank you for your time and reply. Yes, I am trying to include Rd. If I take the node above the test voltage, there are 3 currents going in and out of that node. Rd doesn't seem to be part of any of those three. It also seems that Rd is shorted out due to connecting Vo to ground. How does one incorporate Rd into the equation?

Once again thank you so much.

No problem. The issue is that Vo should be open; it is not shorted to ground. When you calculate the input resistance of a voltage amplifier you need to assume the output is connected to a high impedance. So your third current (that you set to zero) is wrong.

So the KCL equation should be ix = gmvx - vx/ro - (vx-vo)/ro

The second equation you need is vo = ixRl so you have (collecting terms)

ix + (ixRl)/ro = gmvx - vx/ro

Solving, rin = vx/ix = (1 + Rl/ro) / (gm+1/ro)

This is what you expect because if ro is larger than Rl (virtually always the case) then this collapses to 1/(gm+1/ro) ~= 1/gm

Does that make sense now?
 
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  • #5
Yes! Opening Vo fixed everything. I should have tried some more. Thank you.
 
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  • #6
glad I could help. :)
 
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Related to Input Resistance of Common Gate question....

1. What is the definition of input resistance of a common gate?

The input resistance of a common gate is a measure of how much the input signal is attenuated as it passes through the gate. It is also known as the impedance of the gate and is typically measured in ohms.

2. How is the input resistance of a common gate calculated?

The input resistance of a common gate can be calculated by dividing the change in the input voltage by the change in the input current. It can also be calculated by dividing the input voltage by the input current at a specified operating point.

3. Why is input resistance important in common gate circuits?

Input resistance is important in common gate circuits because it affects the gain and stability of the circuit. A lower input resistance can result in a higher gain, but it may also lead to instability and distortion. A higher input resistance can provide better stability, but it may also result in lower gain.

4. How does the input resistance of a common gate affect the overall performance of a circuit?

The input resistance of a common gate can affect the overall performance of a circuit in several ways. It can impact the gain, stability, and bandwidth of the circuit. It can also affect the input impedance, which can impact the ability of the circuit to receive signals from other components.

5. What are some factors that can affect the input resistance of a common gate?

The input resistance of a common gate can be affected by the physical properties of the gate, such as the size and shape of the gate. It can also be affected by the properties of the material used in the gate, such as the conductivity and thickness. Additionally, the operating conditions, such as temperature and voltage, can also impact the input resistance.

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