# Differential amplifier: Our goal is to “spend less, do more!”

The classic four-resistor differential amplifier is shown in Figure 1, but the performance of this circuit may not be as good as the designer wants. Starting from the actual production design, this article discusses some shortcomings related to discrete resistors, including gain accuracy, gain drift, AC common mode rejection (CMR), and offset drift.

The design of a classic discrete difference amplifier is very simple. What is the complexity of an operational amplifier and a four-resistor network?

The classic four-resistor differential amplifier is shown in Figure 1, but the performance of this circuit may not be as good as the designer wants. Starting from the actual production design, this article discusses some shortcomings related to discrete resistors, including gain accuracy, gain drift, AC common mode rejection (CMR), and offset drift.

Figure 1. Classic discrete difference amplifier

The transfer function of the amplifier circuit is:

If R1 = R3 and R2 = R4, Equation 1 simplifies to:

This simplification helps to quickly estimate the expected signal, but these resistances will never be exactly equal. In addition, resistors usually have the disadvantages of low accuracy and high temperature coefficient, which can bring significant errors to the circuit.

For example, using a good operational amplifier and a standard 1%, 100ppm/°C gain setting resistor, the initial gain error can reach up to 2%, and the temperature drift can reach 200ppm/°C. To solve this problem, one solution is to use a monolithic resistor network to achieve precise gain setting, but this structure is bulky and expensive. In addition to low accuracy and significant temperature drift, the CMR of most discrete differential operational amplifier circuits is also poor, and the input voltage range is smaller than the supply voltage. In addition, the monolithic instrumentation amplifier will have gain drift because the internal resistance network of the preamplifier does not match the external gain setting resistance connected to the RG pin.

The best way to solve all these problems is to use a difference amplifier with internal gain setting resistors, such as the AD8271. Usually, these products consist of high-precision, low-distortion operational amplifiers and multiple trimming resistors. By connecting these resistors, a variety of amplifier circuits can be created, including differential, non-inverting, and anti-phase configurations. The resistors on the chip can be connected in parallel to provide a wider range of options. Compared to discrete designs, the use of on-chip resistors can bring many advantages to designers.

Figure 2. Gain error vs. temperature-AD8271 compared to discrete solutions

AC performance

In terms of circuit size, integrated circuits are much smaller than printed circuit boards (PCBs), so the corresponding parasitic parameters are also smaller, which is beneficial to AC performance. For example, the positive and negative input terminals of the AD8271 op amp intentionally do not provide output pins. These nodes are not connected to the traces on the PCB, and the capacitance is kept low, thereby improving loop stability and optimizing common-mode rejection over the entire frequency range. See Figure 3 for performance comparison.

Figure 3. The relationship between CMRR and frequency-AD8271 and discrete solution CMRR comparison

An important function of the differential amplifier is to suppress the common mode signal of the two inputs. Referring to Figure 1, if the resistors R1 to R4 are not completely matched (or when the gain is greater than 1, the ratios of R1, R2 and R3, R4 do not match), then part of the common mode voltage will be amplified by the differential amplifier and used as V1 and V2 The effective differential pressure between appears at VOUT, which cannot be distinguished from the actual signal. If the resistance is not ideal, part of the common-mode voltage will be amplified by the differential amplifier and appear at VOUT as the effective differential voltage between V1 and V2, which cannot be distinguished from the actual signal.

The ability of the differential amplifier to suppress this part of the voltage is called common mode rejection. This parameter can be expressed as Common Mode Rejection Ratio (CMRR) or converted to decibels (dB). The resistance matching of the discrete solution is not as good as the laser adjustment resistance matching in the integrated solution, which can be seen from the relationship curve between the output voltage and CMV in Figure 4.

Figure 4. The relationship between output voltage and common-mode voltage-AD8271 compared to discrete solutions

Assuming an ideal operational amplifier is used, the CMRR is:

Among them, d is the gain of the differential amplifier, and t is the resistance tolerance. Therefore, for unity gain and 1% resistance, CMRR is 50V/V or about 34dB; when using 0.1% resistance, CMRR increases to 54dB. Even with an ideal op amp with infinite common-mode rejection, the overall CMRR will be limited by resistance matching. Some low-cost op amps have a minimum CMRR of 60 dB to 70 dB, making the error worse.

Low tolerance resistance

The amplifier usually performs well within its specified operating temperature range, but the temperature coefficient of the external discrete resistance must be considered. For amplifiers with integrated resistors, the resistors can be drift adjusted and matched. The layout usually places the resistors close to each other, so they will drift together, reducing their offset temperature coefficient. In the discrete case, the resistors are scattered on the PCB, and the matching situation is not as good as the integrated solution, and the resulting offset temperature coefficient will be worse, as shown in Figure 5.

Figure 5. The relationship between system offset and temperature-AD8271 compared to discrete solutions

Whether it is discrete or single chip, four-resistance differential amplifiers are widely used. Since only one device is placed on the PCB instead of multiple discrete components, the circuit board can be constructed more quickly and efficiently, and a lot of area can be saved.

In order to obtain a stable and production-worthy design, the noise gain, input voltage range, and CMR (up to 80dB or higher) should be carefully considered. These resistors are made of the same low-drift film material, so they can provide excellent ratio matching within a certain temperature range.