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# (Exchange of haberdashery) Analysis of principle of differential circuit

2023-11-09【Archive】

The differential op-amp circuit can effectively suppress common mode signal and only amplify differential signal, so it is widely used.

1. Differential Circuit Schematic Configuration

Figure 1. Differential circuit

**Processing target voltage:** is acquisition and processing voltage, such as system bus voltage acquisition and processing, AC voltage acquisition and processing, etc.

**Differential non-inverting/inverting voltage divider resistor:** to obtain a voltage suitable for op-amp processing, it is necessary to divide high voltage signal, as shown in Figure 1, voltage at both ends of V1 and V2 is divided processing, and finally, voltages Vin+ and Vin- suitable for processing by operational amplifier are obtained.

**Differential amplifier circuit:**

Feedback, for an op-amp circuit, op-amp operates in linear region, so there must be negative feedback, no feedback (open loop) or positive feedback, this is a comparator circuit, not an amplifier circuit, while operating time operational amplifier in saturation region or non-linear operating region, due to saturation, output signal is amplitude of supply voltage.

Figure 2 is a positive feedback op amp circuit. Here it cannot be called an op-amp circuit because gain of an open-loop op-amp is ideally infinite. Of course, it is impossible to be infinite in practice, so following structure is a hysteresis voltage comparator, op-amp operates in non-linear or saturation region.

Picture 2

Figure 3 is still structure of voltage comparator. As mentioned above, an op-amp has a large open-loop gain without negative feedback. It operates as a non-linear region and can be used as a voltage comparator.

Picture 3

Op-amp, feedback resistor is connected from output to "-" inverting terminal, which is negative feedback. Of course, when output signal does not exceed supply voltage (Note: power source of all signals is power supply, of course, output cannot exceed amplitude of power supply.), function implemented is signal amplification function, connecting to non-inverting "+" terminal is positive feedback, and circuit function is voltage comparator. Of course, in practice, we do not advocate use of op-amps as voltage comparators, but we use special comparators, such as LM339, LM393, LM211, etc., because operating state of internals of comparators and op amps is still different in practice.

The comparator is connected to current limiting resistors - "R74, R77". This is because comparator charges and discharges capacitive load of next stage with a fast rising or falling edge when switching amplitude. discharge current comes from this active device - comparator, so purpose of adding a current limiting resistor is to prevent effect of current.

**RC filter:** can be adjusted as needed, purpose is to prevent signal distortion such as output overshoot

2. Calculation of differential input voltage

Scheme in figure 4, for ease of calculation, we give each resistance value.

Another feature of differential circuit is symmetry, R40=R56 and R47=R55, and resistances of two branches of differential voltage divider are also equal.

Picture 4

**How are Vin+ and Vin- values calculated? **

First we get by cumbersome calculations, and then we simplify calculations.

First of all, 5 pins of non-inverting end and 6 pins of inverting end of op-amp are obtained with a “virtual short circuit”, where a factor of 6 refers to six 100 kΩ resistors, which is convenient. to simplify formula:

Then get Vin+ via partial pressure ratio:

Get Vin- again via partial pressure ratio:

Then get value of Vin+ minus Vin-.

Actually, **there is another simple method** to get value of Vin+ minus Vin-. Using virtual short circuit characteristic of op-amp, circuit can be equivalent to:

Picture 5

Picture 6

So it's very easy to calculate Vin+ minus Vin-, it's just a simple voltage divider circuit calculated like this:

The resulting differential voltage input is 0.84 V.

Third, calculation of differential amplifier circuit

Picture 7

Derivation of calculation formula still matches virtual short and virtual open characteristics of op-amp. When R56=R40, R47=R55, differential calculation can be simplified as follows:

In actual circuit of application, in order to simplify calculation, we also use simplest calculation method. The circuit that is often used is also above circuit, and resistance is equal to simplify calculation.

Fourth, "offset calculation" of amplifier circuit

**Why bias output voltage? ** This is because when collecting negative values, our sampling chips and microcontrollers are unlikely to support sampling negative values, you need to bias so that output is always positive.

The bias circuit, as shown in Figure 8, connects voltage value at ground of original non-inverting terminating resistor to GND, commonly referred to as bias voltage. So what is final expression?

Picture 8

Using superposition theorem, we finally get:

The formula here ensures that R64=R72, R73=R57, and then a voltage offset of 2.5V_Ref is added to final offset formula on original basis:

As long as an appropriate offset is selected according to actual application, output will always be a positive value.

Picture 9

For example, in diagram in fig. 9, input voltage becomes -100V, and final output voltage is:

In this way, negative voltage is biased to a positive voltage, and processor satisfies processing requirements of processor. The bias circuit is widely used in control circuits such as AC and negative DC voltage.

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