Page 350 - Analog and Digital Filter Design

34
Filter Integrated Circuits

Resistor Value Calculations

The calculation of resistor values has been described in my magazine article.'
Basically the circuit needs to be analyzed in terms of conductance and current
flow through the resistors, since the output voltage is the ratio of two sets of
parallel resistors. The output voltage is always the resistor current from the
supply, divided by the conductance to ground. The current from the supply and
the conductance to ground both depend on how many of the latch outputs are
at logic 0 and how many are at logic 1. If all latches are at logic 1 there is no
path to ground and so the current is zero. Similarly, if all latches are at logic 0
there is no path the positive supply rail and there is no current flow. If some
latch outputs are at logic 1 and some are at logic 0, current will flow, from one
to the other, through the resistors. The output voltage at the resistors' conmon
node (Le., the output) will depend both on the resistor values and the state of
the respective latch output they are connected to.

Resistor values can be found by considering the conductance from the
output to the positive rail, G,, and the conductance between the output and
ground, G,. The current flowing from the positive rail through the resistors is
I= V. G,. where C, is the series connection of G, and G,, and I' is the supply
volt age.

V.Gp .G,
Expanding I = V.Gs gives I =
GP +G,
I
The output voltage is V, = -
Gr
If a substitution into the equation for the resistor current flow is now made:

The total conductance with all resistors in parallel is G, = G,, + Gr.

Tf .G,
Yo =-
G,

The voltage output at reset is zero, since all latches are at logic 0 and there is no
connection to the positive supply. If the phase angle at this point is taken as
being zero, the output of the synthesizer can be expressed as: I% = 0.5V -
0.5V. cos(@), where @is the phase angle and is initially zero. This has been tabu-
lated in Table 14.1 for steps of 18".