“The classic four-resistance differential amplifier can solve many measurement problems. However, there are always applications that require more flexibility than these amplifiers can provide. Because the resistance matching in the differential amplifier directly affects the gain error and the common-mode rejection ratio (CMRR), integrating these resistors on the same die can achieve high performance. However, only relying on the internal resistance to set the gain, users cannot flexibly choose the gain they want outside of the manufacturer’s design choices.

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Author: Rusty Juszkiewicz, Product Engineer

problem:

Can we increase the gain of a fixed gain differential amplifier?

Answer:

Yes, by adding more resistance.

The classic four-resistance differential amplifier can solve many measurement problems. However, there are always applications that require more flexibility than these amplifiers can provide. Because the resistance matching in the differential amplifier directly affects the gain error and the common-mode rejection ratio (CMRR), integrating these resistors on the same die can achieve high performance. However, only relying on the internal resistance to set the gain, users cannot flexibly choose the gain they want outside of the manufacturer’s design choices.

When using fixed-gain amplifiers in the signal chain, if more gain is needed, another amplifier stage is usually added to achieve the required total gain. Although this method is very effective, it will increase overall complexity, required board space, noise, cost, etc. Or, you can choose another method to increase the system gain without adding a second gain stage. By adding several resistors to the fixed gain amplifier to provide a positive feedback path, this can reduce the overall negative feedback, thereby obtaining a higher overall gain.

In a typical negative feedback configuration, the part of the output that is fed back to the inverting input is called β, and the gain of the circuit is 1/β. When β=1, the entire output signal is returned to the inverting input, thereby realizing a unity gain buffer. When the β value is lower, the gain achieved is higher.

Figure 1. Negative feedback: non-inverting op amp configuration.

In order to increase the gain, β must be lowered. This can be achieved by increasing the ratio of R2/R1. However, there is currently no way to increase the overall gain of a fixed-gain differential amplifier by reducing the feedback transmitted to the inverting terminal, because this requires a larger feedback resistance or a smaller input resistance. By providing the output feedback to the reference pin of the differential amplifier, that is, the non-inverting input, the gain of the previous fixed gain amplifier can be increased. The composite feedback coefficient β(βc) produced by this amplifying circuit is the difference between β- and β+, and this coefficient will also determine the gain and bandwidth of the amplifying circuit. Please note that β+ provides positive feedback, so you must ensure that the net feedback is still negative (βC> β+).

Figure 2. Combination β.

In order to use β+ to adjust the circuit gain, the first step is to calculate β- (β of the initial circuit). Note that the attenuation term G_attn is the ratio of the positive input signal of the differential amplifier to the non-inverting input of the operational amplifier.

Once the desired gain is selected, the desired β and β+ can be determined. Because the gain of the fixed gain amplifier is known, β can be easily calculated.

The amount of β+ is exactly the part of the output signal returning to the non-inverting input of the operational amplifier. Remember, the feedback will pass through the β+ path to the reference pin, and the feedback signal will pass through a voltage divider of two resistors (see Figure 3). The resistance of these two voltage dividers must be calculated to achieve the correct β+.

A key characteristic of a differential amplifier is CMRR. The matching of the resistance ratios on the positive and negative networks is critical to achieving excellent CMRR, so the resistor (R5) should also be connected in series with the positive input resistance to balance the increased resistance on the reference pin.

In order to determine the resistances R3 and R4, the Thevenin equivalent circuit can be used to simplify the analysis.

As mentioned above, in order to maintain a good CMRR, R5 must be added. The value of R5 is determined by the parallel combination of R3 and R4, and its coefficient is the same as the resistance in the input attenuator. Because of the ratio of R1/R2 = (1/G_attn) – 1, R1 and R5 can be replaced by R2 and R3||R4 with a fixed ratio respectively.

As mentioned earlier, the gain from VOUT to A_in+ of the simplified circuit must be equal to 1/β+.

Figure 3. Four-resistor fixed-gain differential amplifier: gain adjustment.

Figure 4. Thevenin equivalent circuit.

Figure 5. Simplified positive input resistor network.

Since R3 and R4 pull the operational amplifier, care should be taken not to choose too small values. Once the required load (R3 + R4) is selected, the values of R3 and R4 can be easily calculated using Equation 4. After R3 and R4 are determined, R5 can be calculated using R3||R4 × β.

Because this technique relies on the resistance ratio, it is highly flexible. There is a trade-off between noise and power consumption, and the resistance value should be large enough to prevent the op amp from being overloaded. In addition, since R5 is proportional to R3 and R4, the same type of resistor should be used to maintain good performance at various temperatures. If R3, R4, and R5 drift together, then this ratio will remain unchanged, and due to these resistances, even if there is thermal drift, it will remain at a minimum. Finally, because the gain of the operational amplifier is higher, the bandwidth obtained will be reduced in accordance with the βc/β ratio of the gain-bandwidth product.

AD8479 can realize the typical application of this kind of technology, it is a high common mode difference amplifier of unity gain. The AD8479 can measure differential signals in ±600 V common mode and has a fixed unity gain. Some applications require gains greater than unity gain, so the techniques mentioned earlier are suitable. Another common gain required for current sensing applications is 10, so G1 = 10 can be set.

Since the AD8479 attenuates the common-mode signal, obtains a higher differential signal, and then gains unity system gain, this needs to be considered when implementing gain adjustment.

Since the gain of the positive reference is 60 and the gain of the positive input is 1, the noise gain of the circuit is 61. In addition, since the overall gain is consistent, G_attn must be 1/noise gain:

R3 and R4 can be calculated using Equation 6:

The gain of AD8479 is the specified gain and the load is 2 kΩ, so the target gain of R3 + R4 is as follows.

In order to build this resistor using standard resistance values, it is necessary to use parallel resistors to achieve a more accurate ratio than can be achieved with a single standard resistor.

Figure 6. The final schematic of AD8479 when G = 10.

As can be seen from Figure 7, the output obtained (blue) is 10 times the expected input (yellow).

Figure 7. When G = 10, AD8479 input and output oscilloscope captures.

The nominal bandwidth of a circuit with a gain of 10 should be 1/10 of the typical AD8479 bandwidth. This is because βc/βC = 1/10, and the actual measured C3 dB frequency is 48 kHz.

Figure 8. AD8479 at G = 10: C3 dB frequency.

Figure 9. G = 10: AD8479 in impulse response.

Figure 9 shows that the impulse response and characteristics obtained are consistent with expectations. The slew rate is the same as the standard AD8479 slew rate, but because the bandwidth is reduced, the settling time is longer.

Since the new circuit provides feedback for the two input terminals of the operational amplifier, the common mode of the operational amplifier will be affected by the signals at the two input terminals. This changes the input voltage range of the circuit, so it should be evaluated to avoid overdriving the op amp. In addition, due to the increase in noise gain, the noise voltage spectrum and peak-to-peak value at the output will also increase in the same proportion; however, when the signal is referenced to the input, the effect is negligible. Finally, the CMRR of the circuit with increased gain is equal to the CMRR of the previous circuit (assuming that the R3, R4, and R5 resistors will not add additional common-mode errors). Since R5 is used to modify CMRR with the addition of R3 and R4, CMRR can be tuned to make it better than the original circuit using R5. However, this requires fine-tuning, and in this process, you need to appropriately weigh and adjust the gain error of CMRR.

When implementing this process, you can take advantage of the advantages of a fixed-gain differential amplifier without being limited by its fixed characteristics. Since this technology is universal, it can also be used with many other differential amplifiers. Without adding any active components, simply adding three resistors can achieve higher flexibility in the signal chain, which helps reduce cost, complexity, and circuit board size.

About the Author

Matthew “Rusty” Juszkiewicz is a product engineer in the Linear Products and Solutions (LPS) Division of Analog Devices in Wilmington, Massachusetts. He joined ADI after obtaining a master’s degree in electrical engineering from Northeastern University in 2015. Contact information:[email protected]