Single stage amplifier with current mirror biasing

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SUMMARY

The discussion focuses on analyzing a single-stage amplifier with current mirror biasing, specifically using MOSFETs M1 and M2. The key equations utilized include ID = kn (Vgs - Vth)^2, where VDD is 5V and RC1 is 2k ohm. The participants confirm that the drain current ID,M2 equals 4mA, given that k2 = 2k1 and ID,M1 is 2mA. Additionally, the output resistance in the small signal equivalent circuit is discussed, emphasizing that channel length modulation is equal to zero for both MOSFETs.

PREREQUISITES
  • MOSFET operation principles, including saturation region behavior
  • Understanding of current mirror biasing in amplifiers
  • Basic circuit analysis techniques for amplifiers
  • Small signal analysis of MOSFETs
NEXT STEPS
  • Study the derivation of the output resistance formula for MOSFETs in saturation
  • Learn about the effects of channel length modulation on MOSFET performance
  • Explore common source amplifier configurations and their characteristics
  • Investigate the impact of varying kn values on amplifier gain and performance
USEFUL FOR

Electrical engineering students, circuit designers, and professionals working with analog amplifiers and MOSFET technology.

CKaiL
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Homework Statement


123.jpg


Homework Equations



ID= kn (Vgs - Vth)^2

The Attempt at a Solution



I asked to find the current I D , M2. [/B]

I think in order to solve this question I need to find Vgs but how do I do that?

RC1 = 2k ohm
R = VDD - Vgs / I D ,M2

VDD = 5V , and R = 2k ohm and I have 2 unknown variable. Vgs and I D ,M2

I think i need to make use of this ID= kn (Vgs - Vth)^2 to solve this question
 
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CKaiL said:

Homework Statement


123.jpg


Homework Equations



ID= kn (Vgs - Vth)^2

The Attempt at a Solution



I asked to find the current I D , M2. [/B]

I think in order to solve this question I need to find Vgs but how do I do that?

RC1 = 2k ohm
R = VDD - Vgs / I D ,M2

VDD = 5V , and R = 2k ohm and I have 2 unknown variable. Vgs and I D ,M2

I think i need to make use of this ID= kn (Vgs - Vth)^2 to solve this question
Good idea! But you must first find ID for M1. Combine your last equation with another expression for ID summing currents at the drain.
Then, you assume M1 and M2 have identical I-V characteristics so knowing IDM1 gives you IDM2, and you're done.
 
Could I have more information why the characteristics are identical for M1 and M2? They only have the same value for Vth while their Kn is different by a factor of 2?

I forgot to mention that I D,M1 is also given as 2mA for this question so I D, M2 is also 2mA?
 
CKaiL said:
Could I have more information why the characteristics are identical for M1 and M2? They only have the same value for Vth while their Kn is different by a factor of 2?
I didn't see that, sorry.
I forgot to mention that I D,M1 is also given as 2mA for this question so I D, M2 is also 2mA?
No. For any MOSFET in the 'saturation' region with λ = 0, which this is since Vgs > Vth & Vds > Vgs - Vth),
I = k(Vgs - Vth)2.
So, since k2 = 2k1, what is I,M2 if I,M1 = 2 mA?
 
Hi

So I find the value for Vgs by subbing in Vth and I D,M1. Once I gotten the value of Vgs , i sub this value into the equation to find i D,M2 with a k2? Am I correct?
 
CKaiL said:
Hi

So I find the value for Vgs by subbing in Vth and I D,M1. Once I gotten the value of Vgs , i sub this value into the equation to find i D,M2 with a k2? Am I correct?
No point in solving for Vgs. From my last post it should be obvious that I_M2 = 2I_M1. Solve for I_M1 as I discussed earlier.
 
Sinc k2 = 2k1 , I2 = 2I1. I2 = 4mA?
 
Last edited:
I have another question for this. I am asked to find the small signal parameter of the 2 MOSFET .
The formula are
Output resistance in the small signal equivalent circuit of a MOSFET operating in the saturation region is given as R0 = 1 /(channel length modulation * Current ID)

I have ID value for both 1D M1 and 1D M2 but in this question , channel length modulation for both are equal to 0
when you sub in these value , you will get an error.
 
CKaiL said:
Sinc k2 = 2k1 , I2 = 2I1. I2 = 4mA?
Good guess!
 
  • #10
CKaiL said:
I have another question for this. I am asked to find the small signal parameter of the 2 MOSFET .
The formula are
Output resistance in the small signal equivalent circuit of a MOSFET operating in the saturation region is given as R0 = 1 /(channel length modulation * Current ID)

I have ID value for both 1D M1 and 1D M2 but in this question , channel length modulation for both are equal to 0
when you sub in these value , you will get an error.
Suppose the channel modulation was a very small number but not zero - what would be the output resistance then?
 
  • #11
hmm good guess meaning is ID , M2 = 4mA correct or wrong?

For channel length modulation
In the picture it says that the channel length modulation is equal to 0 for channel length modulation M1 and channel length modulation M2.
 
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  • #12
I would also like to check if this is a configuration of a Common source with source degeneration single stage amlifer?
 
  • #13
CKaiL said:
hmm good guess meaning is ID , M2 = 4mA correct or wrong?
Correct.
For channel length modulation
In the picture it says that the channel length modulation is equal to 0 for channel length modulation M1 and channel length modulation M2.
I know. I asked you what kind of number you would get if the channel modulation was a small number but NOT zero.
 
  • #14
CKaiL said:
I would also like to check if this is a configuration of a Common source with source degeneration single stage amlifer?
What terminal is common to the input and output?
What is the definition of "source degeneration"? You want answers on a platter and we're not allowed to give you that - which is to your benefit.
 
  • #15
The source is connected to the gate and Output is connected to the drain
 
  • #16
CKaiL said:
The source is connected to the gate and Output is connected to the drain
 
  • #17
Yes, but what terminal is common to the input and the output? What is the input referred to, and what is the output referred to?
 
  • #18
Input is connected to the gate , Output is connected to the drain. Source is connected to neither input or output
 
  • #19
I am looking at the amplifier at M2
 
  • #20
CKaiL said:
I am looking at the amplifier at M2
Good.
An input is a voltage. A voltage is always between two points.
An output is also a voltage. Same thing.
So, again - what terminal is common to input and output?
 
  • #21
There don't seem to be a common terminal between the input and output if I look at M2 only.The only common terminal I see between the input and output is between M1 and M2 terminal where the body of the M1 (output) is connected to the input of M1
 
  • #22
CKaiL said:
There don't seem to be a common terminal between the input and output if I look at M2 only.The only common terminal I see between the input and output is between M1 and M2 terminal where the body of the M1 (output) is connected to the input of M1
Talking M2 only. Re-read what I said about how voltages always need two points.
The input is between G and S.
The output is between D and S.
See any common terminal yet?
 

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