Page 160 - DSP Integrated Circuits

4.15 Wave-Flow Building Blocks 145

4.15.1 Circuit Elements
The input impedance to an open-circuited unit element (a f-domain capacitor)
with ZQ=R is, according to Equation (4.34),

Using Equation (4.27) we get the reflectance,

and

The input impedance to a short-circuited unit element (a f-domain inductor)
with ZQ = R is, according to Equation (4.35),

The reflectance is

and

Figure 4.25 shows the two
types of f-domain elements and
their corresponding wave-flow
equivalents. An open-ended unit
element corresponds to a pure
delay while a short-circuited unit
element corresponds to a delay
and a 180-degree phase shift.
The reflectance for a unit
element terminated at the far
end by a resistor with ZQ = R
(matched) is Figure 4.25 Lossless transmission lines that are
open- and short-circuited at the far
end and the corresponding wave-flow
equivalents

Hence, an input signal to
such a unit element is not
reflected. The corresponding
wave-flow equivalent, shown to
the right in Figure 4.26, is a
wave sink.
A short-circuit has the reflec- Figure 4.26 Wave-flow equivalent for a resistor
tance