# Terminating a differential-input signal

-September 25, 2003

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.

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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.

 References Mancini, Ron, "Fully differential amplifiers and transmission lines," EDN, Aug 7, 2003, pg 20. Karki, James, Fully Differential Amplifiers, SLOA054D, Texas Instruments, January 2002.

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