Download CMOS Source Resistance and Effects on Source Follower Gain

CMOS Source Resistance and Effects on Source
Follower Gain
Introduction
The source follower is a difficult device to design using a CMOS device as the
transconductance of CMOS device is low compared to that of a BJT, therefore non
conventional followers have to be designed to give a gain close to 1, as the Gain of a
simple common drain follower is much less than 1. But after analysis it is not only the
transconductance that affects the gain of the amplifier with shrinking semiconductor
processes and smaller devices, the source resistance (Rs) is also contributing to the
drop in gain.
Measurement of Gain
The circuit below shows a simple common drain amplifier used to measure
Gain.
VDD
Vin
M1
Vout
RL
Figure 1: Test Circuit
From figure 1 the following small signal model can be drawn:
V(d)
n
Vin
gm’
Rds
V(g)
V(s’)
Rs
V(s)
Vout
RL
Figure 2: Small Signal Model of figure 1
From figure 2 it can be shown that the Gain of a simple Common Drain follower is:
Gain =
1
1 + (gL + gds)
gm’
Using a TSMC 0.18um process with a CMOS device (M1: figure1) having the
following dimensions Width =5um, Length = 0.18um, the following results were
obtained, with a 100mV ac waveform at 10KHz.
V(g)dc = 1.2V
Expected Gain = 0.836
Measured Gain = 0.655
V(g)dc = 1.0V
Expected Gain = 0.749
Measured Gain = 0.63
V(g)dc = 0.9V
Expected Gain = 0.703
Measured Gain = 0.612
V(g)dc = 0.75V
Expected Gain = 0.631
Measured Gain = 0.56
It can be seen from the results above that there is an extra loss in Gain, this factor
being the source resistance (Rs).
Calculating Source resistance (Rs).
Using the small signal model used in figure 2 and now calculating the DC solution for
it as shown in the diagram below:
VDD
I(d)
I(d’)
Vin
gm’
V(d)
n
Rds
V(g)
V(s’)
Rs
V(s)
Vout
RL
Figure 3: Simple Common Drain Follower (DC Model)
By using the model figure 3 above, the following parameters can be extracted from
simulation:
1)
2)
3)
4)
5)
I(d) measured DC current.
V(s) Voltage of the source.
Vin.
VDD.
Rds drain/source resistance.
From these the intrinsic gm’ can be calculated using:
gm’ = 2
B.I(d’)
I(d’) is simply:
I(d’) = I(d) – I(rds)
Where:
I(rds) =
VDD – V(s)
Rds
Assuming that Rds >> Rs
And:
B(Beta) =
Uo.Cox.W
2L
Note: That the intrinsic gm’ can only be measured using the measured DC current on
account that Vgs’ can not be measured without the source resistance (Rs).
Now using the small signal model (figure 2) the following equation can be derived
taking into account the effects of gm’ by the drain/source resistance (Rds) as shown
above:
Rs =
gm’.RL – G(1 + gm’.RL)
G.gm’
Where G = Vout
Vin
Measuring Source Resistance (Rs)
Using the same Transistor as per the Gain measurements ie. Width = 5um, Length =
0.18um. input ac waveform 100mV at 10KHz.
The following results were obtained:
V(g)dc = 1.2v:
I(d) = 364uA;
gm’ = 2.75mA/V;
Rs = 370ohms.
V(g)dc = 1.0v:
I(d) = 251uA;
gm’ = 2.26mA/V;
Rs = 357ohms.
V(g)dc = 0.9v:
I(d) = 197uA;
gm’ = 1.99mA/V;
Rs = 357ohms.
V(g)dc = 0.75v:
I(d) = 119uA;
gm’ = 1.52mA/V;
Rs = 375ohms.
Conclusion
From the results it can be seen that Rs is real and has a major effect on the gain of a
source follower, the results show a 5% spread in the value of Rs this is probably due
to the estimates of the value of Rds when simulated. It is also worth mentioning that
the value of Rs will affect the value of the calculated transconductance as the true
Vgs’ used to calculate gm is in fact smaller than the measured Vgs due to the
existence of Rs.
Also from measuring a transistor of width 5um to 10um, Rs would be expected to
halve, this was not the case and the measurements highlighted that the values were
similar in value, after further investigation it was found that the design kit used based
it’s calculations on a minimum source area, and without the addition of BSIM
parameters to the transistor model; Rs will be inaccurately calculated and simulated in
the majority of cases. This will mean there will always be a mismatch between real
silicon and simulation when measuring such things as transistor transconductance.