Time domain reflectometry 

In this look at transmission line theory, we will assume an RG-58 type of coaxial cable which has a characteristic impedance of 50 Ω. Where we let C stand for the capacitance per unit length, 30 pF per foot in this case, the characteristic impedance Zo = sqrt(L/C) where L is the inductance per unit length. This gives L = Zo²×C = 75 nH per foot.

We make a very simplistic MultiSim SPICE model of the transmission line being driven by a 50-Ω source impedance of the left in the Figure 1 with a load resistance whose value we are going to set to several different values, to 10,000 Ω, to 50 Ω, and then to 5 Ω while we examine the effects of each as a study of time domain reflectometry (TDR).

Figure 1 TDR result from a MultiSim SPICE model of a transmission line driven by a 50-Ω source impedance (R1) and where load resistance, R2, is set 10,000 Ω.

In Figure 1, using a square wave signal source, we see the signal takes 16.5 ns to make its way down the transmission line to arrive at R2. During that time, the signal input end at V1 and R1 presents an input impedance of 50 Ω, the cable’s characteristic impedance Zo.

Since the R2 value does not match Zo, energy transfer into R2 is incomplete and some of the arriving energy gets reflected back toward the left again. When that reflection reaches R1 in another 16.5 ns—a total transit time of 33 ns—the impedance presented to the V1 and R1 pair jumps up and we see the input voltage at the left end of the transmission line jump up too.

The propagation velocity and the velocity factor of the transmission line are calculable from the transit times are nearly two-thirds the speed of light in free space, just as in the published data for this cable.

In Figure 2, when we have R2 at 50 Ω, there is a match to Zo and no energy gets reflected back again. When we have R2 at only 5 Ω, we have a mismatch to Zo again and a reflection back toward the left, but the impedance at the left end drops instead of rising.

Figure 2 TDR Results for load R2 = 50 Ω, showing a match with no energy reflected back, and for R2 = 5 Ω showing a mismatch and energy reflected back.

Of course, this SPICE model is very crude in that each LC pair represents one foot of cable length. A more finely grained model with many more LC pairs per unit length would yield better waveform results than we’ve shown here.

For the sake of illustrating these principles though, I beg your forgiveness.

John Dunn is an electronics consultant, and a graduate of The Polytechnic Institute of Brooklyn (BSEE) and of New York University (MSEE).

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