8.3.2.3 Resistor Design Equations for Single-to-Differential Applications

Being familiar with the FDA resistor selection criteria is still important because the LMH5401 gain is configured through external resistors. The design equations for setting the resistors around an FDA to convert from a single-ended input signal to a differential output can be approached in several ways. In this section, several critical assumptions are made to simplify the results:

• The feedback resistors are selected first and are set to be equal on the two sides of the device.
• The DC and AC impedances from the summing junctions back to the signal source and ground (or a bias voltage on the non-signal input side) are set equal to retain the feedback divider balance on each side of the FDA.

Both of these assumptions are typical and are aimed to deliver the best dynamic range through the FDA signal path.

After the feedback resistor values are selected, the aim is to solve for R_T (a termination resistor to ground on the signal input side), R_G1 (the input gain resistor for the signal path), and R_G2 (the matching gain resistor on the non-signal input side); see Figure 61. This example uses the LMH5401, which is an external resistor FDA. The same resistor solutions can be applied to AC- or DC-coupled paths. Adding blocking capacitors in the input-signal chain is a simple option. Adding these blocking capacitors after the R_T element (see Figure 61) has the advantage of removing any DC currents in the feedback path from the output V_OCM to ground.

Figure 61. AC-Coupled, Single-Ended Source to a Differential Gain of a 4-V/V

Most FDA amplifiers use external resistors and have complete flexibility in the selected R_F. However, the LMH5401 has small on-chip feedback resistors that are fixed at 25 Ω. The equations used in this section apply with an additional 25 Ω to add to the external R_F resistors.

After the feedback resistor values are selected, solve for R_T (a termination resistor to ground on the signal input side), R_G1 (the input gain resistor for the signal path), and R_G2 (the matching gain resistor on the non-signal input side). The same resistor solutions are applied to AC- or DC-coupled paths. Adding blocking capacitors in the input-signal chain is a simple option. Adding these blocking capacitors after the R_T element has the advantage of removing any DC currents in the feedback path from the output V_OCM to ground.

Earlier approaches to the solutions for R_T and R_G1 (when the input must be matched to a source impedance, R_S) follow an iterative approach. This complexity arises from the active input impedance at the R_G1 input. When the FDA converts a single-ended signal to a differential signal, the common-mode input voltage at the FDA inputs must move with the input signal to generate the inverted output signal as a current in the R_G2 element. A more recent solution is shown as Equation 3, where a quadratic in R_T is solved for an exact required value. This quadratic emerges from the simultaneous solution for a matched input impedance and target gain. The only required inputs are:

1. The selected R_F value.
2. The target voltage gain (A_V) from the input of R_T to the differential output voltage.
3. The desired input impedance at the junction of R_T and R_G1 to match R_S.

Solving this quadratic for R_T starts the solution sequence, as shown in Equation 3:

Equation 3.

Because this equation is a quadratic, there are limits to the range of solutions. Specifically, after R_F and R_S are selected, there is physically a maximum gain beyond which Equation 3 starts to solve for negative R_T values (if input matching is a requirement). With R_F selected, use Equation 4 to verify that the maximum gain is greater than the desired gain.

Equation 4.

If the achievable A_Vmax is less than desired, increase the R_F value. After R_T is derived from Equation 3, the R_G1 element is shown in Equation 5:

Equation 5.

Then, the simplest approach is to use a single R_G2 = R_T || R_S + R_G1 on the non-signal input side. Often, this approach is shown as the separate R_G1 and R_S elements. This approach can provide a better divider match on the two feedback paths, but a single R_G2 is often acceptable. A direct solution for R_G2 is shown as Equation 6:

Equation 6.

This design proceeds from a target input impedance matched to R_S, signal gain A_V, and a selected R_F value. The nominal R_F value selected for the LMH5401 characterization is 152 Ω (R_FExternal + R_FInternal, where R_FInternal is always 25 Ω). As discussed previously, this resistance is on-chip and cannot be changed. See Table 1 and Table 2 in the Frequency Response section, which lists the value of resistors used for characterization in this document.