# NMOS current mirror

The simple MOS current mirror, the staple ingredient of the analog IC design kitchen. Device sizes are taken from our book reference.

# Circuit Netlist

```* dev <nets>        <values>
* --------------------------
V1    n_pos 0       1.3V
I1    n_pos n1      50uA
V2    n2    0       0.6302654V
M1    n1    n1 0 0  nmos w=5u l=2u
M2    n2    n1 0 0  nmos w=5u l=2u
```

# 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.

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

```n1 = 0.63027
n2 = 0.63027
n_pos = 1.3
v1#branch = -50.0 uA
v2#branch = -49.989 uA
(v2#branch/v1#branch) = 0.99977
```

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

```device            m2            m1
model          nmos          nmos
gm    347.132 uS    347.132 uS
rds     920.43 kR     920.43 kR
id     49.991 uA     49.991 uA
vgs     0.63026 V     0.63026 V
vds     0.63026 V     0.63026 V
vth     0.38804 V     0.38804 V
vdsat     0.22641 V     0.22641 V
```

As seen given our equal Vds for both source and mirror transistors, both branches are very well matched in performance.

## DC Analysis (Sweep)

However, in a real life scenario our load could vary widely hence degrading our current match. For this purpose, in our DC analysis, we are measuring the variation of the mirrored output current under different applied loads.

We are applying a DC sweep to V2 (our load voltage) from 0 to 1.3V in 0.05V increments and plotting the output current magnitude vs drain voltage. (our load voltage at n2)

As can bee seen our current matching has degraded given finite Rout of the output transistor.

# Results

For the Simple NMOS Current Mirror:

• VMIN: The absolute minimum voltage needed for the mirror to be in the saturation region is its Vdsat (roughly a Veff) at the nominal 50uA mirror current i.e:
Vmin_abs = Vdsat = 0.22641V
• However in practice the current mirror requires at least a 0.35V load voltage to be operational with the maximum r_out performance (this can be seen from the plot above). Note lower compliance voltages may be achieved through the use of wider devices.
• The variation of the drain current with changes in load voltage is as follows:
Error Measurement: Variation of 49.473uA to 50.566uA over an operating range of 0.35 to 1.3V. This is equivalent to an error of 1.093uA or 2.186% 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, as shown in the PMOS mirror in subsequent sections.

## Figures of Merit

Output Resistance Rout: 869.17kΩ (measured from 0.35 to 1.3V linear range). Note this is roughly consistent with our device output resistance (rds) parameter seen above.

Compliance Voltage: 0.35V (from ground). Defined here as the minimum voltage that guarantees the r_out performance of the mirror.

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