Lab 6 - ECE 421L 

Authored by Nicholas Banas,

Banasn1@unlv.nevada.edu

3/19/15 

  

This lab covers the gain, input and output resistance of several different amplifier topologies.

Measurement Methodology 

  Calculating the gain of an amplifier seems to be fairly straightforward, measure the input and output voltages and divide.  However while conducting this experiment we ran into noise factors that influenced measurements.  To account for this we took both pk-pk and amplitude measurements.  Using the amplitude removes the overshoot from the measured signal, basically ignoring the noise in the waveform.  For calculations we will use the amplitude measurements as they more accurately represent the actual gains.

  Calculating input resistance is more difficult.  It requires finding the input voltage and input current.  As this lab does not have any current probes, we are required to use a test resistor in series with the input and differential voltage measurements over the test resistor to calculate the input current.  To achieve a small error margin we tried to use a test resistor that was very close to the expected input resistance of the amplifier.

  Calculating the output resistance is very similar to calculating the input resistance.  The major difference is where to input the signal.  We measured the output resistance by first grounding the input.  Then we put a test voltage (in series with a test resister equal to the expected output resistance) into the output of the amplifier.

  A note on polarized capacitors:  It is important to remember during this experiment that polarized capacitors should not be reversed biased.  The construction of electrolytic film capacitors causes them to delaminate when exposed to moderate reverse voltages and they can explode.  In the amplifiers used in this lab this means that any polarized capacitors should be connected with the positive terminal to the input or output.  this is because the DC voltage is much higher at these nodes than at the function generator.    

Source Follower

We used the following circuits for our source follower  amplifiers.  The left is a NMOS based design while the left is PMOS based.  


 
The gain for the topology is calculated by using (vin-id*R2)*gm = id and id*R2 = vout (R6 for the PMOS) to come up with Av = R2/(1/gm+R2).  Because the slope of the transconductance for the 3306 series MOSFETs in the Id range that we are using (~5m) is so high, it is hard to come up with a usable number just from the datasheet.  The Rin and Rout calculations are shown in the following table.
  
NmosPmos
Gain:

Measured Av=
Vout/Vin = 0.922

Measured gm =
1/(R2/Av-R2) = 11.8mA/V 		Gain:

Measured Av =
Vout/Vin = 0.804

Measured gm =
1/(R6/Av-R6) = 4.1mA/V
Rin estimate ~
R1||R3
~33.3k

Measured Rin ~
33.3k/(V1/V2-1)
~ 34k
Rin estimate ~
R4||R5
~33k

Measured Rin ~
33.3k/(V1/V2-1)
~54k
Rout estimate ~
R2||1/gm
~100

Measured Rout~
100/(V1/V2-1)
~135
Rout estimate ~
R6||1/gm
~100

Measured Rout~
100/(V1/V2-1)
~193
  

Common Source

We used the following circuits for our common source amplifiers.  The left is a NMOS based design while the left is PMOS based.
 

 
  The gain for the topology is calculated by using (vin-id*Rsn)*gm = id and id*R8 = vout to come up with Av = R8/(1/gm+Rsn).  
It is clear that as Rsn is increased, the gain will be reduced.  The input resistance is calculated the same as with the source follower.  The output resistance is R8||(1/gm+Rsn||R2).
 
NmosPmos
Gain:

Measured Av=
Vout/Vin = 5.4

Measured gm =
1/(R8/Av-Rsn) = 11.8mA/V		Gain:

Measured Av=
Vout/Vin = 3

Measured gm =
1/(R7/Av-Rsp) = 4.3mA/V
Rin estimate ~
R1||R3
~33.3k

Measured Rin ~
33.3k/(V1/V2-1)
~ 31k		Rin estimate ~
R4||R5
~33.3k

Measured Rin ~
33.3k/(V1/V2-1)
~ 39k
Rout estimate ~
R8||(1/gm+Rsn||R2)
~1k

Measured Rout~
1k/(V1/V2-1)
~852		Rout estimate ~
R8||(1/gm+Rsn||R2)
~1k

Measured Rout~
1k/(V1/V2-1)
~923
  

Common Gate

 We used the following circuits for our common gate amplifiers.  The left is a NMOS based design while the left is PMOS based.
 

 
  The gain for the topology is calculated by using vin*gm*(R2||(ro+R8))/(Rsn+R2||(ro+R8)) = id and id*R8 = vout.  The first equation is ~ Vin*gm*R2/(Rsn+R2), using this to come up with Av = R2*R8*gm/(Rsn+R2).  Rsn is currently in the non-dominate term in the denominator so it has minor effect on the gain.  As long as Rsn<<R2 it will continue have little effect on the gain.  Rin is calculated as Rsn+R2||(1/gm+R8).  The output resistance is R8||(1/gm+Rsn||R2).
 

NmosPmos
Gain:

Measured Av=
Vout/Vin = 4.9

Measured gm ~
Av*(Rsn+R2)/R2*R8
gm ~ 5.39mA/V		Gain:

Measured Av=
Vout/Vin = 2.52

Measured gm ~
Av*(Rsp+R6)/R6*R7
gm ~ 2.99mA/V
Rin estimate =
Rsn+R2||(1/gm+R8)
~200

Measured Rin ~
200/(V1/V2-1)
~ 31k		Rin estimate =
Rsn+R2||(1/gm+R8)
~330

Measured Rin ~
330/(V1/V2-1)
~ 31k
Rout estimate ~
R8||(1/gm+Rsn||R2)
~1k

Measured Rout~
1k/(V1/V2-1)
~949		Rout estimate ~
R8||(1/gm+Rsn||R2)
~1k

Measured Rout~
1k/(V1/V2-1)
~973
 

Push-Pull

We used the following circuits for our Puss-Pull amplifier.
 
 
 
 For this circuit we calculate the -Vin*gmp=id and id= vin*gmn+vout/R1 which leads to -R1(gmn+gmp)=Av.  As R1 increases, the Av also increases. Note, for the experiment a 1/511 divider was used on the input.
 
Push-Pull
Gain for R1=100k:
Calculated Av = R1(gmn+gmp) ~ 1.6Kv/v

Measured = 511*Vout/Vin = 647v/v
Gain for R1=510k:
Calculated Av = R1(gmn+gmp) ~ 8Kv/v

Measured = 511*Vout/Vin = 935v/v