Bias and Current Mirrors Interview Questions

No. The copy is exact only when the output voltage equals the gate voltage, because then both devices see the same V_DS. Elsewhere channel-length modulation changes the current. With 2/0.15 µm devices the output is 21.8 µA at 0.9 V and 11.5 µA at 0.2 V, where the device leaves saturation. The output resistance, here 70.7 kΩ, is the slope that sets this error.

The reference device is diode-connected, so its V_DS equals V_GS. The output device has the same V_GS. When its drain also sits at V_GS, the two devices are in the same state and carry the same current. The lesson checked this: the 8/1 µm mirror gives exactly 20 µA at 0.714 V.

The copy rises above the reference, because channel-length modulation adds current as V_DS grows. The error is about ΔV divided by V_A, the Early voltage. A short device has a small V_A, so its error is large. A longer device or a cascode makes it small.

A cascode device on top raises the output resistance by about (g_m + g_mb)·r_o. In the lesson it went from 0.80 MΩ to 102 MΩ. The price is headroom: the output now needs about V_GS + V_Dsat, around 0.85 V. A wide-swing version gets most of the gain back while the output can fall to about 0.3 V.

The ground at each block is a little different, because supply current flows through the metal. The copy changes by about (g_m/I_D)·ΔV for a ground difference ΔV. Here g_m/I_D is the transconductance per unit of drain current. So send a current to each block and mirror it locally instead. A current does not care about the ground voltage on the way.

A separate diode device biases the cascode gates. It is sized so the bottom devices sit just above V_Dsat. The textbook W/4 rule comes from the square law, and in sky130 it left the copy 12 % low. A cascode on the reference side makes both bottom devices see the same V_DS and fixes the copy. Then sweep the output to find where the current is 1 % low, at every corner.

In the plain wide-swing mirror the reference device is diode-connected, so its V_DS is V_GS. The output's bottom device sits near V_Dsat instead. Different V_DS means a different current. A cascode on the reference side holds its bottom device at the same low V_DS as the output side. Then both carry the same current.

In the lesson the W/4 rule left the copy 12 % low. Short sky130 devices do not follow the square law, so the bottom devices end up at the wrong V_DS. The bias width trades output resistance against the lowest output voltage. So find it by sweeping, and check the copy at the target output range.

Write each requirement as one line with a limit and a measurement, set after measuring a reference design at every corner. Use one bench per check. Run a supply sweep and a temperature and supply sweep for the worst case. Add an output sweep for compliance and power-up transients, fast and slow. A constant-g_m reference moves its current on purpose, so specify the tail current as a band.

The circuit has two DC solutions: the working state and a zero-current state where every branch carries nothing. The operating point found the working state. The power-up transient from 0 V stays in the zero state, at about 48 pA. A start-up circuit must push the loop out of zero and then switch itself off. Test it with a supply ramp, at every corner and at the coldest temperature.

Each branch's current comes only from the other branch through the mirrors. If one branch carries nothing, the mirror copies nothing to the other, and that is self-consistent. The working state is the second consistent point. Nothing in the circuit prefers one over the other at power-up.

op and dc report only the working state, so a DC run looks fine. Run a power-up transient from 0 V with a ramped supply. Repeat it at every corner, with fast and slow ramps and at the coldest temperature. Cold leakage is smallest, so a slow ramp there no longer hides the zero state.

Supply sensitivity is the relative change in current per relative change in supply. A plain resistor gives 1, and a resistor into a diode gave 1.59 in the lesson. The beta multiplier gave 0.241, because a PMOS mirror forces equal currents and the supply enters only through finite r_o. The price is the second, zero-current state.

It keeps injecting current into the loop, so the reference current is no longer set only by the resistor. It also burns standing current all the time. Check both on the bench: the reference current with and without the start-up, and the current the start-up branch draws. In the lesson that branch drew 0.64 µA and the reference current did not change.