NMOS source degenerated current mirror

An improvement to the output resistance of the simple MOS mirrors can be attained by the addition of source resistors. The addition of a source resistor introduces negative feedback. Note the following:

1. An increase in load voltage leads to an increase in mirror current (due to the finite output resistance of the mirror)
2. The above current error leads to an increase in voltage at the source resistance
3. The increase in source voltage results in a reduction in Vgs for the mirror
4. In turn, this acts to reduce the mirror current via the gm of the transconductor and hence
5. A reduction in current error for a given change in load voltage
6. Result: an increase in output resistance, increased by gm x Rs
```r_out = ro x (1 + gm x Rs) + Rs = ro + ro (gm x Rs) + Rs
```

In other words, the gain of the negative feedback loop (which corrects the current error) is proportional to the value of the source resistance times the gain of the transconductor, but alas the larger the resistance the more it consumes voltage headroom.

In this schematic, we have maintained the NMOS size from the simple MOS article (to illustrate the trade-off above) and added 3KR source resistances. We have reduced the resistance values relative to our book reference due to our reduction in supply.

Circuit Netlist

```* dev <nets>        <values>
* --------------------------
I1    n_pos n1      50uA
V1    n_pos 0       1.3V
V2    n2    0       0.8225957V
M1    n1    n1 n3 0 nmos w=5u l=2u
M2    n2    n1 n4 0 nmos w=5u l=2u
R1    n3    0       3kR
R2    n4    0       3kR
```

SPICE Simulations

Walking through our simulation results we have:

Operating Point Analysis

Nominally with matched output load voltage (matched Vds across output transistor), calculating the operating point DC voltages and currents for our mirror.

Relevant source code lines:

```OP
print all

* Output current over constant input current (with matched vds load): should be 1 for best match.
print (v2#branch/v1#branch)
```

Operating point DC measurement results (re-formatted for display and analysis):

```n1 = 0.8226 V
n2 = 0.8226 V
n3 = 0.14997 V
n4 = 0.14997 V
n_pos = 1.30 V
v1#branch = -50.0 uA
v2#branch = -49.983 uA
(v2#branch/v1#branch) = 0.99966
```

And our relevant transistors' device parameters at the DC OP (re-formatted for display and analysis):

```device            m2            m1
model          nmos          nmos
gm     340.72 uS     340.72 uS
gmbs     93.793 uS     93.793 uS
rds     971.53 kR     971.53 kR
id     49.987 uA     49.987 uA
vgs     0.67262 V     0.67262 V
vds     0.67262 V     0.67262 V
vbs    -0.14997 V    -0.14997 V
vth     0.42592 V     0.42592 V
vdsat     0.23153 V     0.23153 V
```

DC Analysis (Sweep)

For measuring the variation of the mirrored output current under different applied loads. We apply a DC sweep to V2 (our load voltage) from 0 to 1.3V in 0.05V increments.

We are plotting the output current magnitude vs drain voltage. (our load voltage at n2)

Relevant source code lines:

```DC V2 0V 1.3V 0.05V          ; Sweep Drain voltage from 0v to 1.3v in 0.05v increments.
...
gnuplot \$filename (v2#branch*-1e+06) ylimit \$ylow \$yhigh xlimit \$xlow \$xhigh xdelta \$xdel title \$title xlabel \$xlabel ylabel \$ylabel
```

As before our current matching has degraded given finite Rout of the output transistor but to a much lesser extent.

Results

For the Simple MOS Current Mirror from our reference, now with the addition of source degeneration we can make the following observations:

• The absolute minimum voltage needed for the mirror to be in the saturation region is it's Vdsat (roughly a Veff) plus the drop accross the source resistor at the nominal 50uA mirror current i.e:
Vmin_abs = 0.23153 + 0.14997 > 0.3815 V
• However in practice the current mirror requires at least a 0.45V load voltage to be operational with its maximum Rout (this can be seen from the plot above where the slope is linear).
• Error Measurement: Variation of 49.6uA to 50.159uA over a linear operating range of 0.45 to 1.3V. This is equivalent to an error of 0.559uA or 1.118% relative to our current reference.
Note that this topology is symmetrical and can be inverted by using PMOS transistors connected to the positive supply rail instead. (in this case however due to lower holes mobility at large channel lengths, PMOS device widths need to be sized much larger to attain the same Veff)

Figures of Merit

Output Resistance Rout: 1.5206MΩ (measured from 0.45 to 1.3V linear range).

Compliance Voltage Vmin: 0.45V (from ground)

In summary,

Current Mirrors Performance Summary
Topology Vmin (V) Compliance Voltage (V) r_out (kΩ) Current Consumption (uA) Area (um^2)
Simple NMOS 0.226 0.35 869.17 50 20
NMOS Source Degenerated 0.3815 0.45 1521 50 20 + 2 x A_res