# NMOS 4T resistor-biased cascoded current mirror

As discussed in other articles, there are different ways we can generate our cascode bias voltage, one way to do this is via use of an additional current branch and a thin diode-connected device (as shown in the NMOS diode-biased cascoded current mirror article), another more traditional alternative (as shown on the NMOS 3T resistor-biased cascoded current mirror) is by making use of a resistance in-branch to generate the cascode bias (one shortcoming of the latter is the 3T asymmetry which leads to systematic offset between bias and mirror branches). The 4T topology below overcomes this asymmetry (among other benefits) and is usually used instead as it can be very well matched in practice.

In general, the 4T resistor-biased topology is typically a good fit in cases where one has access to high-R resistors in the technology kit and can afford the area needed for the resistor. In such a scenario this traditional 4T R-based topology can be superior as it allows for good control for the cascode bias, it saves the additional current needed for the diode and in many cases leads to less variability over PVT (although this depends on many factors).

As before our cascoded rout is approximately given by:

```r_out = ro2 x a3 = ro2 x (gm3 x ro3)
```

# Circuit Netlist

```* dev <nets>        <values>
* -----------------------------------
I1    n_pos n3      50uA
V1    n_pos 0       1.3V
V2    n2    0       0.5210533V
R1    n3    n1      4.4kΩ
M1    n4    n1 0  0 nmos W=20u L=3u
M2    n5    n1 0  0 nmos W=20u L=3u
M3    n2    n3 n5 0 nmos W=10u L=0.35u
M4    n1    n3 n4 0 nmos W=10u L=0.35u
```

# SPICE Simulations

## Operating Point Analysis

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

```n1 = 5.210533e-01
n2 = 5.210533e-01
n3 = 7.410507e-01
n4 = 2.673797e-01
n5 = 2.673795e-01
vp = 1.300000e+00
v1#branch = -50.00 uA
v2#branch = -49.98 uA
(v2#branch/v1#branch) = 0.9996
```

And our relevant transistor' device parameters at the DC OP (re-formatted for display)

```device  m4          m3          m2          m1
model   nmos        nmos        nmos        nmos
gm      859.89  uS  859.89  uS  552.844 uS  552.844 uS
gds     150.089 kR  150.089 kR  218.435 kR  218.435 kR
id      49.979  uA  49.980  uA  49.984  uA  49.984  uA
vgs     0.4737  V   0.4737  V   0.5210  V   0.5210  V
vds     0.2537  V   0.2537  V   0.2674  V   0.2674  V
vth     0.4536  V   0.4536  V   0.3880  V   0.3880  V
vdsat   0.0787  V   0.0787  V   0.1471  V   0.1471  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)

## Monte Carlo Analysis

In our Montecarlo analysis, we are measuring the effect of transistors’ random mismatch on the output current of our mirror (i.e. how small random variations in individual transistor parameters when added together can result in an overall output current error).

Further details concerning Montecarlo simulation settings have been described under the NMOS 3T resistor-biased cascoded current mirror article and also apply here.

# Results

For the cascode current mirror, we can make the following observations (note these are very similar to our diode-based cascoded design as we have tried to match bias and sizing to allow us to compare across).

• The absolute minimum voltage needed for the mirror output branch to be in the sat region is the vdsat of both mirror and cascode devices: vmin_abs = 0.147 + 0.079 >> 0.226
• However as shown with the current sizing, the mirror requires at least ~0.4 load voltage to yield its maximum Rout. (seen from the plot above where the slope is linear).
• Error Measurement: We see a variation of 49.97267uA to 49.99331uA over a performance operating range of 0.4 to 1.3V.

## Figures of Merit

Output Resistance Rout: 43.60MΩ (measured from 0.4 to 1.3V linear range).

Compliance Voltage Vmin: ~0.4V (from ground)

In summary,

Current Mirrors Performance Summary
Topology Vmin (V) Compliance Voltage (V) r_out (kΩ) Bias Current (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_r3k
NMOS 3T Res-biased Cascoded 0.221 0.5 18911 50 123.5 + 1 x A_r10p7k
NMOS 4T Res-biased Cascoded 0.226 0.4 43605 50 127 + 1 x A_r4p4k