SBOS710D October 2014 – February 2018 LMH5401
PRODUCTION DATA.
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:
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.
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:
Solving this quadratic for R_{T} starts the solution sequence, as shown in 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.
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:
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:
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.