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, V_N=V_P, 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 R_T. The equation for the terminating-resistor value follows:

where R_S is the driver/source termination resistor.

You must account for the source output impedance, R_S, and the cable-termination resistance, R_T, in the gain equation, because they are parts of gain-setting resistors R₁ and R₃ (R_G in the general case). Begin the gain-resistor calculations by using Thevenin's theorem to obtain a series-equivalent circuit to replace R_T and R_S. Thevenin-equivalent voltage and resistance equations for a series model follow:

Substituting these three equations into the ideal gain equation, V_OUT=V_IN (R_F/R_G), yields the gain equation for a circuit with significant source/termination impedance. This equation applies to fully differential inputs and outputs; hence, R_G=R₁=R₃, and R_F=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 R_G, use that value to calculate R_T, and then use the values for R_T and R_G to calculate the feedback-resistor value. An appropriate feedback-resistor value for an op amp in this frequency range is 500Ω. R_T approximately equals R_S, 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 R_G=(R_F/2)=249Ω (closest 1% standard value). Now, use the first equation to calculate R_T=55.6Ω and select R_T as the closest 1% standard value, 56.2Ω. An algebraically manipulated equation follows, which solves for R_F=495.5Ω, and the closest 1% standard value is 499Ω.

Figure 2 shows the complete circuit with the calculated resistor values.

Author Information

Ron Mancini is staff scientist at Texas Instruments. You can reach him at 1-352-569-9401, rmancini@ti.com.