The Circuit Designer's Companion - diagramas.diagram...

Grounding and wiring 37times will damp the response. The only way to avoid it completely is to consider everyinterconnection as a transmission line, and to terminate each end with its correctcharacteristic impedance. Very fast circuits are designed in exactly this way; designersof slower circuits will only meet the problem in severe form when driving long cables.The uses of mismatchingMismatching is not always bad. For instance, a very fast, stable pulse generator can bebuilt by feeding a fast risetime edge into a length of transmission line shorted at the farend (Figure 1.28), and taking the output from the input to the line. A 1m length of coaxwith velocity factor 0.66 will give a 10ns pulse.Z oZ oDt = [2 · D · √ε r / 3.10 8 ]Figure 1.28 Pulse generation with a shorted transmission line1.3.3 Frequency domainIf you are more interested in radio frequency signals than in digital edges you want toknow what a transmission line does in the frequency domain. Consider the transmissionline of Figure 1.26 being fed from a continuous sine-wave generator of frequency f andmatched to the line’s Z o . Again, the energy can be thought of as a wave propagatingalong the line until it reaches the load; if the load impedance is matched to Z o then thereis no reflection and all the power is transferred to the load.If the load is mismatched then a portion of the incident power is reflected backdown the line, exactly like an applied pulse edge. A short or open circuit reflects all thepower back. But the signal that is reflected is a continuous wave, not a pulse; so thevoltage and current at any point along the line is the vector sum of the voltages andcurrents of the forward and reflected waves, and depends on their relative amplitudesand phases. The voltage and current distribution down the length of the line forms a socalled“standing wave”. The standing wave patterns for four conditions of linetermination are shown in Figure 1.29. You can verify this experimentally with a lengthof fairly leaky coax and a “sniffer” probe, connected to an RF voltmeter, held close toand moved along the coax.Standing wave distribution vs. frequencyNote that the standing wave distribution depends on the wavelength of the appliedsignal and hence on its frequency. Standing waves at one frequency along a givenlength of line will differ from those at another. The standing wave pattern repeats itselfat multiples of λ/2 along the line. The amplitude of the standing wave depends on thedegree of mismatch, which is represented by the reflection coefficient Γ, the ratio ofreflected current or voltage to incident current or voltage. Standing wave ratio (s.w.r.)is the ratio of maximum to minimum values of the standing wave and is given bys.w.r. = (1 + |Γ|)/(1 - |Γ|) = R L /Z o for a purely resistive terminationThus an s.w.r. of 1:1 describes a perfectly matched line; infinite s.w.r. describes a line