Keywords: amplifier gain fixed gain problem:

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

Answer:

Yes, by adding more resistors.

The classic four-resistor differential amplifier can solve many measurement challenges. However, there are always applications that require more flexibility than these amplifiers can provide. Since resistor matching in differential amplifiers directly affects gain error and common-mode rejection ratio (CMRR), integrating these resistors on the same die can achieve high performance. However, relying solely on internal resistors to set the gain gives the user the flexibility to 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 required, another amplifier stage is usually added to achieve the desired overall gain. While this approach is very effective, it adds to the overall complexity, required board space, noise, cost, etc. Alternatively, you can choose another method to increase the system gain without adding a second gain stage. By adding a few resistors to the fixed gain amplifier to provide a positive feedback path, this reduces the overall negative feedback, resulting in 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 implementing a unity gain buffer. At lower values of beta, higher gains are achieved.

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

In order to increase the gain, β must be decreased. This can be achieved by increasing the R2/R1 ratio. However, there is currently no way for a fixed-gain difference amplifier to increase the overall gain by reducing the feedback transmitted to the inverting terminal, because this requires the use of a larger feedback resistor or a smaller input resistor. The gain of the previous fixed-gain amplifier can be increased by providing output feedback to the reference pin of the difference amplifier, the non-inverting input. The composite feedback coefficient β(βc) produced by this amplifier is the difference between β- and β+, and this coefficient will also determine the gain and bandwidth of the amplifier. Note that β+ provides positive feedback, so it must be ensured that the net feedback remains negative (β – > β+).

Figure 2. Combinatorial beta.

In order to use β+ to adjust the circuit gain, the first step is to calculate β- (the β of the initial circuit). Note that the attenuation term G_attn is the ratio of the positive input signal of the difference amplifier to the noninverting input of the op amp.

G0 = G_attn × noise gain noise gain = 1/β– β– = G_attn/G0β– = G_attn/G0(1)

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.

βc = G_attn/G1 βc = β– – β+ β+ = G_attn(1/G0 – 1/G1)(2)

The amount of β+ is exactly the portion of the output signal that returns to the non-inverting input of the op amp. Remember, the feedback goes through the β+ path to the reference pin, and the feedback signal goes through a voltage divider of two resistors (see Figure 3), which must be calculated to achieve the correct β+.

A key characteristic of a difference amplifier is CMRR. Matching the resistor ratio on the positive and negative nets is critical to achieving good CMRR, so the resistor (R5) should also be in series with the positive input resistor to balance the added resistance on the reference pin.

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 with the same factor as the resistor in the input attenuator. Because of the ratio R1/R2 = (1/G_attn) - 1, R1 and R5 can be replaced by R2 and R3||R4, respectively, with a given ratio.

Let (1/G_attn) – 1 = α(3)

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

Vth × α/(α + 1) = VA_in+ because VA_in+/VOUT = β+ where β+ = G_attn(1/G0 – 1/G1) R4/(R3 + R4)) = (1/α) × (1/ G0 – 1/G1)(4)

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 op amp, care should be taken not to choose values that are too small. Once the desired 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 by using R3||R4 × β.

Because this technique relies on resistance ratios, it is highly flexible. There is a trade-off between noise and power dissipation, and the resistor value should be large enough to prevent overloading the op amp. Also, since R5 is proportional to R3 and R4, the same type of resistor should be used to maintain good performance over a wide range of temperatures. If R3, R4, and R5 drift together, this ratio will remain the same, and due to these resistors, even with thermal drift, it will be kept to a minimum. Finally, since the gain of the op amp is higher, the obtained bandwidth is reduced by the ratio βc/β of the gain-bandwidth product.

A typical application of this technique is the AD8479, which is a unity-gain high common-mode difference amplifier. The AD8479 is capable of measuring differential signals at ± 600 V common mode and has a fixed unity gain. Some applications require a gain greater than unity, making the previously mentioned techniques well suited. Another common gain required for current sensing applications is 10, so let G1 = 10.

Since the AD8479 attenuates the common-mode signal, resulting in a higher differential signal, and then a unity system gain, this needs to be taken into account when implementing the 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. Also, 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 the AD8479 is the specified gain and the load is 2 kΩ, so the target gain for R3 + R4 is as follows.

Let R3 + R4 = 2000 , R4 = 30, R3 = 1970 , R5 = 1773(8)

In order to build this resistor using standard resistor values, parallel resistors are required to achieve a more accurate ratio than can be achieved using a single standard resistor.

Let R3 = 2050, R4 = (32.4 || 866 ), R5 = (1910 || 54900)(9)

Figure 6. Final schematic of the AD8479 with G = 10.

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

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

The nominal bandwidth of a circuit with a gain of 10 should be 1/10 the bandwidth of a typical AD8479 because βc/β– = 1/10, while the –3 dB frequency actually measured is 48 kHz.

Figure 8. G = 10: AD8479 at –3 dB frequency.

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

Figure 9 shows that the obtained impulse responses and characteristics are as expected. The slew rate is the same as the standard AD8479 slew rate, but requires longer settling time because of the reduced bandwidth.

Because the new circuit provides feedback for both inputs of the op amp, the common mode of the op amp is affected by the signals at both inputs. This changes the input voltage range of the circuit, so it should be evaluated so as not to overdrive the op amp. In addition, as the noise gain increases, the noise voltage spectrum and peak-to-peak value at the output also increases by 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 do not add additional common-mode error). Since R5 is used to correct the CMRR with the addition of R3 and R4, the CMRR can be tuned to be better than the original circuit using R5. However, this requires fine-tuning, and in the process, you need to properly weigh and adjust the gain error of the CMRR.

When implementing this process, you can take advantage of the fixed gain differential amplifier without being limited by its fixed characteristics. Since this technique is universal, it can also be used with many other differential amplifiers. The simple addition of three resistors allows greater flexibility in the signal chain without adding any active components, which helps reduce cost, complexity, and board size.