Terminating a differential-input signal
A previous column explains that terminating transmission lines at the driving and receiving ends minimizes signal reflections (Reference 1). You must calculate termination-resistor values for single-ended and fully differential circuits. The calculations for single-ended circuits are simple; the noninverting-circuit configuration separates the termination and gain-setting resistors. The calculations in fully differential circuits are complicated, because you can't separate the termination and gain-setting resistors (Figure 1).
Assuming that you're dealing with an ideal op amp simplifies the calculations; doing so makes the amplifier gain infinite with no frequency degradation. Under these assumptions, VN=VP, causing a virtual short across the op-amp inputs. Thus, R1 is effectively in series with R3, and the series combination is in parallel with RT. The equation for the terminating-resistor value follows:
where RS is the driver/source termination resistor.
You must account for the source output impedance, RS, and the cable-termination resistance, RT, in the gain equation, because they are parts of gain-setting resistors R1 and R3 (RG in the general case). Begin the gain-resistor calculations by using Thevenin's theorem to obtain a series-equivalent circuit to replace RT and RS. Thevenin-equivalent voltage and resistance equations for a series model follow:
Substituting these three equations into the ideal gain equation, VOUT=VIN (RF/RG), yields the gain equation for a circuit with significant source/termination impedance. This equation applies to fully differential inputs and outputs; hence, RG=R1=R3, and RF=R2=R4.
A design example calculates resistor values for a common circuit with a 50Ω differential-balance source and an overall differential gain of one (Reference 2). First, choose a value for RG, use that value to calculate RT, and then use the values for RT and RG to calculate the feedback-resistor value. An appropriate feedback-resistor value for an op amp in this frequency range is 500Ω. RT approximately equals RS, so the gain through the termination resistors is about 0.5. The op-amp gain must be two to achieve an overall gain of one, so begin the calculations with RG=(RF/2)=249Ω (closest 1% standard value). Now, use the first equation to calculate RT=55.6Ω and select RT as the closest 1% standard value, 56.2Ω. An algebraically manipulated equation follows, which solves for RF=495.5Ω, and the closest 1% standard value is 499Ω.
Figure 2 shows the complete circuit with the calculated resistor values.