There is an occasional caution that even unity-gain stable Voltage Feedback Amplifiers (VFAs) risk instability in inverting attenuator applications (Reference 1). In fact, there should be no more instability risk there than operating non-inverting gain of 1 as long as no other added poles around the loop introduce adequate phase shift to move into instability. Example inverting attenuator designs with both unity gain, and decompensated, VFAs will be shown with paths to degrade, then improve, the phase margin. Then, assuming an inverting attenuation stage is safe stability wise, you can use these in some cases to incrementally improve the SNR for a two-stage amplifier design.

**Inverting Attenuators using VFA – Noise Gain (NG) and Loop Gain (LG) Considerations.**

Any stability concern in an op amp application essentially comes down to assessing the phase margin at LG = 0dB crossover (Reference 2). In the classic Bode analysis, this is looking at the open loop gain and phase for the core amplifier (A_{ol}) then laying the NG on top of the magnitude plot and subtracting its phase from the A_{ol} phase. Where the NG crosses over the A_{ol} magnitude (LG = 0dB), the total phase around the loop needs to have adequate margin to -180deg to insure stability. The NG is then the key element determined by the external configuration. That NG is simply the inverse of the transfer function from the op amp’s output pin to the differential input voltage. With V+ grounded in an inverting configuration, Equation 1 shows that simple divider for the simple attenuator of Figure 1 (the examples here are using non-Rail-to-Rail output stage devices to keep a simpler open loop output impedance).

Then, inverting Equation 1 will give the NG of Equation 2.

In the LG analysis, the voltage source input is grounded. The example of Figure 1 has a DC noise gain of 1.25V/V. So, if the op amp itself is unity gain stable, inverting attenuators should be stable as well (Section 18, Reference 3). The two sources of confusion in Reference 1 are:

- Assuming the NG is the same as the signal gain (Rf/Rg) neglecting the 1+ part of the correct NG.
- It is easy to reduce phase margin in an inverting attenuator using higher Rf values, and/or with faster op amps, where an added loop pole is created with the op amps’ parasitic input capacitance.

Figure 1 does show about 3.5dB peaking in the closed loop response suggesting a phase margin of 42deg (Figure 2, Reference 2). Here, since the TINA (Reference 4) model for the OPA890 (Reference 5) did not include the specified input capacitance (check that using Reference 6), that 1.5pF was added externally causing the simulated peaking.

**Figure 1**

This lower phase margin is not due to the DC noise gain being too low for this device, but instead the feedback pole caused by C_{p}. This effect is usually easy to fix for a design using a unity gain stable op amps using a feedback capacitor and the pole/zero cancellation idea setting 1/(R_{g}C_{p}) = 1/(R_{f}C_{f}). This is identical to the scope probe flatness adjustment idea (section 13, Reference 3). Adding a feedback capacitor equal to 4*C_{p} gives the flat response of Figure 2. This very flat response is bandlimited to 36MHz by the feedback pole in the signal path but clearly also has much higher phase margin over the simple starting point of Figure 1. If higher bandwidth is required, simply scale the R_{g} and R_{f} resistors down in the same ratio.

**Figure 2**

Setting up a LG phase margin simulation for Figure 1 (Reference 2) showed a LG = 0dB frequency at 81MHz with 41degrees phase margin. Repeating that with the C_{f} = 6pF added in Figure 2 increased the LG = 0dB frequency to 88MHz with 64degrees phase margin.