The differential outputs provided by fully differential amplifiers (FDA) can be used in a positive feedback scheme to generate a partially active output impedance. Applying this technique, to set the isolating resistor in a typical RC filter at a Successive Approximation Register (SAR) ADC input, provides an ancillary advantage. Many designs buffer the FDA input resistors with precision low power Rail-to-Rail (RR) op amps. These buffers are often much lower in bandwidth than the requisite FDA bandwidth to drive the SAR sampling events. The system harmonic distortion limits might well rest at the outputs of these buffers if asked to drive too low an input resistor as part of the FDA design. One outcome of implementing an active output resistance in the FDA is to also scale up the required input resistor to hit the same gain. This technique can be used to hit the same design targets providing lighter loading on the lower speed input stage buffers possibly improving the overall system THD. The requisite design equations for the FDA and example designs will be shown.

**Low power, high impedance buffered, single or differential in to differential out SAR interface. **

Emerging precision wideband FDAs (1) provide many useful features in driving 16- to 20-bit differential input SAR ADCs. FDAs intrinsically look like differential inverting op amps with an added output common mode control loop. They always present a relatively low input resistor that must be driven. Commonly, designs will buffer an unknown source impedance with a standard precision op amp using it to drive the FDA input resistor. A relatively complete design example is shown in Figure 1. This will be modified to reduce the loading on the OPA376 (2) outputs while retaining the same design targets.

**Figure 1**

**Buffered single or differential input to differential output SAR ADC input driver.**

For this example, a SAR Vref = 4.5V has been assumed. This then requires a 9Vp-p differential signal for full scale where placing that around a 2.25V common mode voltage is easily achieved using the Vcom pin of the THS4551 FDA.

Some of the features in this initial example design include:

- The inputs include overdrive protection to ground and the +3.3V supply used for the OPA376 buffers. Those BAV99 diodes are current limited by series 499Ω resistors which then also form a 200kHz bandlimiting pole at the op amp inputs. Using a lower supply on the input buffers guarantees the THS4551 cannot be overdriven.
- Like many RR I/O op amps, the OPA376 has more linearity on the output than input pins. Here, a full scale 0 to 2V input range is assumed to stay below the input stage crossover at 1V below the 3.3V supply – retaining the best input offset voltage. Setting a gain of 1.5V/V, the OPA376 outputs provide a full 0 → 3V swing with good headroom using the -0.23V negative supply (3) and 3.3V positive supply. At the maximum 3V output, those feedback and gain resistors require 1mA of output current back to ground.
- To take the full 6Vp-p differential swing available at the outputs of these two input buffers, the FDA is configured for a gain just slightly below 1.5X to deliver a maximum differential swing of 8.98Vp-p to the ADC. This would occur for the two inputs swinging 180
^{o}out of phase 0 to 2V. - The FDA feedback resistors are selected very near the recommended 1kΩ value. This required the input resistor (what the OPA376 must drive) to be 681Ω. With the upper channel input at 2V and the lower at 0V, the FDA summing junctions are at 1.8V forcing the lower OPA376 to sink 1.8V/681 = 2.6mA load current.
- The output RC network is very typical of high resolution SAR ADC requirements. The 2.2nF differential capacitor and 24.9ohm isolating resistors form another 1.45MHz pole.

The relatively low 681Ω load resistor for the OPA376 (or dual OPA2376) may be too low for the desired harmonic distortion using this low power input stage. Also, the max load currents will slightly reduce their available linear output swing. One easy option is to simply scale the FDA resistors up in the same ratio. This is often a good solution but here the FDA resistors are selected to both add negligibly to the total FDA noise contribution and retain good phase margin. Simply doubling them will impair both – but might still be acceptable for many applications. The option considered here is to implement a partially active output impedance which will also have the effect of raising the input resistor that needs to be driven by the precision input buffers. While the OPA376 is an excellent choice for a low noise and power precision input stage, Table 1 shows a few similar alternates devices.

**Table 1**

**Alternate choices to the OPA376 input buffer. **

Similarly, while the THS4551 is a very good SAR driver selection, Table 2 shows some alternate selections.

**Table 2**

**Alternate choices to the THS4551 precision FDA**

**Implementing an active output impedance using positive feedback in the FDA**

Another new capability offered by the FDA is the ability to simply implement active impedances through positive feedback since both output polarities are readily available. An earlier article explored (4) this to provide an active match to a doubly terminated transmission line when the load is fixed. This was intended to reduce the required output voltage swing at the FDA pins to improve headroom. Figure 2 shows the intended topology for application as an ADC driver having only an RC filter load to the ADC differential inputs. The design equations will vary slightly from (4) as the load is not a fixed resistance.

The modified FDA circuit of Figure 2 will be used to replace the simple output stage design of Figure 1 with the same gain and output impedance. A similar 1.0kΩ feedback resistor is being used but the output resistors (R_{o} ) have been cut in approximately half to a standard 12.1Ω value. The positive feedback resistors (R_{p} ) and the new nearly doubled R_{g} resistors are exact in Figure 2, but would need to be taken to standard values. The values shown have been set to give the same gain and to double the physical 12.1Ω output resistors to 24.2Ω on each side at low frequencies using positive feedback.

**Figure 2**

**Active output impedance circuit to drive the SAR ADC**

To arrive at the design equations for R_{p} and R_{g} , solve for the output impedance and gain assuming the load is open at DC. As the capacitor impedance decreases at higher frequencies, both the gain and output impedance will also decrease. Defining a ratio, α, as the ratio of total output impedance (on each side) to the physical resistor (R_{o} ), and picking an R_{f} value along with a target voltage gain (A_{v} ), the required equations can be derived.

The positive feedback resistor is set by Equation 1. Note here an α =1 (no magnification of the physical output resistor) will solve for Rp → ∞.

The positive feedback acts to increase the signal gain where now the required “gain” resistor is also magnified as given by Equation 2. This acts to decrease the loading on the input buffer stage incrementally improving its harmonic distortion and output swing range.

Ignoring the relatively small Ro terms here, this very nearly scales the R_{g} by just the desired output impedance scaling term (α). Figure 3 shows an output impedance simulation with the 2.2nF capacitor removed. That 33.7dBohms at lower frequencies is the desired 48.4Ω differential output impedance. It does start to deviate above 10MHz, but the positive feedback actually goes away as the final load capacitor shorts out transitioning the circuit to simple FDA driver with 12.1Ω output on each side.

**Figure 3**

**Active output impedance for the FDA design**

These benefits for the input stage are offset by an increase in the Noise Gain for the FDA stage. That will act to incrementally reduce the Loop Gain (increasing harmonic distortion in this stage) and increase the noise contribution in the FDA stage. The THS4551 is already far lower harmonic distortion than the OPA376 (and all other devices in Table 1 except the OPA837 and ADA4805). Direct comparisons are not easily extracted from the data sheets, but at 1kHz, 2.8Vp-p into 10kΩ the OPA376 shows -111dB THD. Figure 4 repeats Figure 18 from the THS4551 datasheet (2) showing less than -120dBc at 100kHz for 2Vpp into 1kΩ across gain settings. The OPA376 will almost certainly be the limit to HD performance in this design and increasing its load resistance should move in the direction of better THD through the entire channel.

**Figure 4**

**THS4551 100kHz HD2 and HD3 across gain setting at 2Vpp into 1kΩ load.**

Evaluating the topology of Figure 2 for the noise gain (NG) gives Equation 3. Note that if R_{p} were infinite (no positive feedback), this would reduce to the standard NG equation.

Evaluating this for the example design (α=2) of Figure 2 shows the noise gain has increased from the 2.5V/V in the simple design of Figure 1 to 4.5V/V. Table 3 summarizes some performance metrics for the just the two FDA design options. The SNR comparisons are using 9Vp-p maximum output (or 3.18Vrms in the noise setup in TINA (5)).

**Table 3**

**Some performance metrics for the two possible FDA designs**

The bandwidth being set by the output RC remained identical but the SNR did degrade with the active output impedance approach while the phase margin improved. Combining these two options with the OPA376 input stage will give the more complete comparison in Table 4. This slight drop in SNR may be acceptable to improve the harmonic distortion out of the first stage with the lighter loading. Combining the amplifier SNR with a typical 92dB SAR ADC SNR shows only a 0.45dB degradation going to the active output impedance approach in this example.

**Table 4**

**Full channel comparisons between simple and active Z _{o} options. **

**Conclusion**

A new option to driving the RC load in a SAR driver application using the positive feedback approach with an FDA has shown some benefits in moving the load impedance up for the prior stage. This comes at the cost of incrementally higher noise in the overall channel aiming for the same design targets. Simply scaling the Rs up in the FDA stage can also work. This will also increase the noise and often causes a loss of phase margin. Using an active output impedance approach will scale up the input resistor possibly with improved phase margin in the FDA stage. Different design targets using different combinations of input amplifiers and FDAs should consider this option if it seems the input stage distortion would improve with a load resistor that can be scaled using the active output impedance option with the FDA.

**Active output impedance references**

- TI, THS4551, “Low Noise, Precision, 150-MHz, Fully Differential Amplifier”
- TI, OPA376, “Precision, Low Noise, Low Iq Operational Amplifier”.
- TI, LM7705, “Low Noise Negative Bias Generator”
- J. Karki, Analog Applications Journal, 1Q2009, page29, “Output impedance matching with fully differential operational amplifiers”
- TINA simulator available from DesignSoft for less than $350 for the Basic Plus edition. Includes a wide range of vendor op amps and is the standard platform for TI op amp models.

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