Two Way Street
Suppose that I offered you a new highway-traffic monitor that reports total traffic density on a section of roadway. It counts eastbound traffic as positive flow, westbound traffic as negative, and sums the two figures. It does not provide separate figures for the two directions. If the two flows are the same in magnitude, the sensor reports zero. Would you buy it?
Obviously, this sensor reveals only part of the
total traffic picture. Transmission lines, like streets, support traffic in two
directions. A voltage probe connected to a transmission line acts much like a
traffic-density sensor. It shows an aggregate-voltage waveform but doesn't say which way the waveform is moving. If two waveforms cross, sometimes the voltage probe reports zero.
For example, Figure 1 shows
the composite voltage (pink) at capacitor C3 (Eye
of the Probe, EDN 12/1/2006). The waveform shows a 200-psec step
followed by a negative bump at B. To decipher the cause of that bump, include in
your schematic a virtual (nonphysical) 0-Ω resistor, R0. Set all the
parasitics associated with that component to their minimum values.
Export from your simulator both the voltage, v0, at
R0 and the current, i0, flowing through
R0. Then, use the equations in Figure 1 to
compute both forward- and reverse-moving waveforms, vF and vR, respectively. The composite waveform at C3 is
the sum of these two waveforms. The forward waveform (blue) appears ideal. The
negative bump appears only in the reverse waveform (purple). Therefore, the bump
must be a reflection coming from something to the right of
C3.
Next, consider the shape and timing of the reflected bump.
The bump duration is comparable with the signal rise time, so you may conjecture
that it comes from one localized spot. The center of the bump occurs 400 psec
after the midpoint of the initial rising edge. That 400-psec number is a
round-trip reflection delay, so the imperfection you seek must be 200 psec
downstream from R0. The only significant imperfection near that
location is the receiver-load capacitance, C4. If you remove
C4 from the circuit, the bump disappears, confirming C4 as
the source of the bump. A thorough examination of vR reveals a
second negative bump, smaller than the first, coincident with the main signal
edge. That reflection comes from the C3.
If this technique seems new or unusual to you, think back to when you were a little kid. Didn't your mother tell you to look both ways for traffic?