The main characteristics and transconductance voltage analysis of MOS tube differential amplifier

Differential amplifiers are widely used in analog integrated circuits. For example, the input stage of integrated operational amplifiers adopts the circuit structure of differential amplifiers. This is because the differential amplifier only amplifies the differential signal and suppresses the common mode signal. It has strong anti-interference ability, and has the advantages of small source shift and easy direct coupling between stages. This section will discuss the main performance of the MOS tube differential amplifier.

(1) The main performance of MOS tube differential pair tube

The MOS differential pair tube is shown in Figure 2.5-1. M1 and M2 in the figure are completely symmetrical (matched), and their working currents (ID1, ID2) are provided by the current source IO. The output current ID1 and ID2 depend on the difference of the input voltage (VG1-VG2), but the sum of ID1 and ID2 is always equal to the current source IO, and the drains of M1 and M2 are connected to resistive loads or MOS transistor active loads, respectively , Which constitutes a differential amplifier, which converts current output into voltage output to achieve voltage amplification.

1. The DC special conversion characteristics of the MOS differential pair tube

The input difference voltage VID of the differential pair tube can be expressed as

The β of the above formula is

The relationship between the output current ID1 and ID2 of the current source Io is

Substituting (2.5-3) into (2.5-1) formula, after sorting out, get ID1 and ID2 as

From this, the output current difference ΔID is obtained. for

It can be seen from the above formula that when the input difference voltage VID is equal to zero, the output difference current ΔID is zero. when，ΔID is the maximum value, and its value is equal to Io. Therefore, the range of VID can be expressed by the following formula:

The conversion characteristic curve of the MOS differential pair tube ΔID-VID can be drawn from the formula (2.5-6), and the curve is shown in Figure 2.5-2.

It can be seen from the conversion characteristic curve of the MOS differential pair tube that it is similar to the bipolar differential pair tube, and it also has limiting characteristics. Its linear working range (2.5-7) depends on the working current Io and the channel of the M1 and M2 tubes. The width-to-length ratio (W/L) generally ranges from 300 millivolts to several volts, which is much larger than the linear range of the bipolar differential pair tube (about 50 millivolts).

2. Transconductance gm of MOS differential pair tube

By (2.5-6), the double-ended output transconductance of the differential pair tube in balance can be obtained. According to the definition,

And the single tube transconductance of M1 (or M2) is

It can be seen that the transconductance of the double-ended output of the differential pair tube (when balanced) is the same as the transconductance of the M1 or M2 tube, which is consistent with the result of the bipolar differential pair tube. The transconductance value of the MOS tube is much lower than that of the bipolar transistor, and it is proportional to the square root of the operating current.，the transconductance of the bipolar transistor is proportional to the operating current。

3. The input offset voltage of the MOS differential pair tube

When the differential pair tube M1 and M2 are symmetrical, the input offset voltage Vos is equal to zero. Now we discuss the mismatch of the differential pair tube M1 and M2. When the threshold voltage VT of the two tubes are inconsistent, the input offset voltage caused by the inconsistency of the channel's width-to-length ratio is Vos (regardless of load matching). The input offset voltage of the differential pair tube is defined as: when the drain current ID1 of M1 and M2 is equal to ID2, the difference in VGS voltage caused by the unequal parameters of M1 and M2，that is, the offset voltage of the tube.

When the parameters  of M1 and M2 are not equal, ID1 and ID2 can be written as

At this time ID1 and ID2 should be equal, they are

Suppose again

Substituting (2.5-11~13) equation into (2.5-10) equation, after calculation and finishing, the offset voltage VGS can be obtained as (using

 known

Find the derivative of the β relation (when calculating, regarded as a constant), you can write

After substituting it into equation (2.5-14), we get

In the formula, gm is the transconductance when the MOS differential pair tube is double-ended output.

From the above formula, the following conclusions can be obtained:

(1) The input offset voltage of the MOS differential pair tube is proportional to the difference between the threshold voltages of the two MOS tubes M1 and M2. The greater the threshold voltage of the MOS tube, the greater the difference and the greater the offset voltage of the circuit. . The threshold voltage of MOS tube is generally in the range of several volts, so its offset voltage is larger than that of bipolar transistor. In order to reduce the offset voltage, the threshold voltage of the MOS tube must be lowered, and an ion implantation process is used to make the threshold voltage of each MOS tube more consistent, thereby reducing the threshold voltage difference.

(2) Increase the channel width and channel length of the MOS differential pair tube, adopt a reasonable layout, and improve the lithography accuracy, so that the ΔL/L and ΔW/W errors can be reduced, and the offset voltage can be reduced.

According to equation (2.5-16), the temperature coefficient of the offset voltage can also be calculated, that is, the temperature drift of the offset voltage:

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