Designing of a CMOS Differential Amplifier

A differential amplifier is a circuit whose output voltage is directly proportional to the difference between voltages applied at it’s to inputs. Ideally, this amplification of voltage difference is useful in eliminating noise signal which is common to both the inputs i.e. a Common Mode Rejection Ratio of infinity. A typical CMOS differential amplifier circuit is shown below.

Fig.1 — CMOS Differential Amplifier Circuit

All MOSFETs are in saturation. Also, we can see from the circuit that MOSFETs 3 and 4 act as a current mirror, hence are of the equal dimensions. That’s the case with MOSFETs 5 and 6. For simplicity, let’s assume that MOSFETs 1 and 2 are of equal dimensions too. The output Vout is taken across the load capacitor C and is proportional to (Vin1 — Vin2).

THE METHOD

STEP 1 — To find DC current from Slew Rate

Slew rate is the rate of change of output voltage of the amplifier due to a step change in input voltage. It occurs in the extreme case of a branch being open circuited (say MOSFETs 1 and 3).

Fig.2 — Current flowing through MOSFETs 2 and 4 when MOSFETs 1 and 3 are in cut-off region.

Figure 2 shows that the load capacitor C charges through MOSFET 4 (pMOS) and discharges through MOSFET 2 (nMOS). Hence the capacitor acts as a current sink while charging and as a current source when discharging.

STEP 2 — To find aspect ratios of MOSFETs 3 and 4 from Input Common Mode Range

Let the input common mode range be Vcmax to Vcmin. Let Vin2 be grounded and Vin1 be equal to Vcmax. Also, assume that source terminal of MOSFET 1 is grounded, so as to find the minimum drain voltage of MOSFET 1 for it to remain in saturation (the actual drain voltage will be higher as the source will not be grounded).

Fig.3 — Branch containing MOSFETs 1 and 3

Where Vth is the threshold voltage of MOSFET 1. The body terminal of the nMOS is grounded but the source terminal is not. Hence, there will be a voltage difference between body and source. Therefore, there exists a small difference in the actual threshold voltages of MOSFETs 1 (nMOS) and 3 (pMOS) because of body effect.

STEP 3 — To find aspect ratios of MOSFETs 1 and 2 from Gain-Bandwidth Product

Fig.4 — The small signal model of a differential amplifier.

In Fig.4, ro2 and ro4 are the output resistances of MOSFETs 2 and 4 respectively, gm is the transconductance of MOSFET 2, Vin is the differential input voltage and Vo is the output voltage.

STEP 4 — To find aspect ratios of MOSFETs 5 and 6 from Input Common Mode Range

Fig.5 — A portion of the circuit showing MOSFETs 1 and 5

In conclusion, when the capacitance of load capacitor C is known, the slew rate S, gain bandwidth product GBP, and input common mode range [Vcmin, Vcmax] are specified, a differential amplifier can be designed using these steps by finding D.C. current i and aspect ratios of all the MOSFETs. The gain provided by a differential amplifier is not as large as required by an Op-Amp. Hence the Differential Amplifier stage is followed by a Gain stage to form a Transconductance Amplifier, which is then followed by a Buffer stage to form an Operational Amplifier.