ECE3434
Table-defined band-pass profiles
Version 2.11
Value: 105 pts
Standardized frequency profiles such as Butterworth and Chebychev can be entirely defined from the
low-pass tables for simple RLC doubly-terminated ladders via a procedure that is readily constructed
in pSPICE schematics. Of the standardized profiles, band-pass profiles are one of the more common
extensions, for which we transform each reactive component of the RLC ladder into a pair of
components as illustrated by figure FP-2.1:
Figure FP-2.1: LP:BP conversion. ω0 = normalized frequency = 1r/s and BW = normalized
bandwidth. The components are defined in a ‘pSPICE-ready’ form.
So for a low-pass form represented by an RLC ladder, as in the example represented by the (3rd-order
Chebyshev) figure FP-2.2, they can be converted using the conversions to a bandpass form, as
represented by figure FP-2.3
Figure FP-2.2: RLC doubly-terminated ladder for 3rd-order 1-dB Chebyshev low-pass. This
circuit was constructed from the ‘table values’ components of figure FP-2.1.
Figure FP-2.3: RLC doubly-terminated ladder for 3rd-order 1-dB Chebyshev band-pass.
This circuit was constructed from the ‘converted values’ components of figure FP-2.1 in the form of
figure FP-2.2 and is ‘pSPICE ready’.
This circuit can be converted to an active form by a number of techniques, but the most compact one
is of the ‘Leapfrog form’ represented by figure 24.6-9 in your Professor Notes, chapt 24, for which
series- and parallel- groups of components are converted into a series of transfer functions for TY
alternated with TZ , using the Delyannis-Friend single-amplifier biquad topology as indicated by the
forms of figure FP-2-4.
Figure FP-2.4a: DF biquad topology equivalent to series RLC, normalized to ω0 = 1.0r/s.
This circuit is ‘pSPICE ready’. All that is then necessary is to provide values (or parametric
functions) for Q and for k1.
Figure FP-2.4b: DF biquad topology equivalent to either parallel LC or series LC,
normalized to ω0 = 1.0r/s. This circuit is ‘pSPICE ready’. All that is then necessary is to provide
values (or parametric functions) for Q and for k2.
Assembling the circuit in leapfrog topology is a matter of combining FP-2.4a and FP2-4b and
identifying appropriate values for k1, k2, (and k3) which will match to the circuit of figure FP-2.3
Figure FP-2.5: Bandpass leapfrog realization for 3rd –order profile. This realization elects the equal
capacitance simplification for which Cz = 1/(2Q) for each DF Biquad (same as Q1 = Q2 = Q3).
Once you have defined k1, k2, and k3, (if you cannot see them distinctly in this figure the same figure
exists in Professor Notes, Ch24, as figure 24.6-9) this circuit will be ‘pSPICE ready’ and should have
exactly the same profile as that of figure FP-2.3. It most likely will be convenient to use several
parameter calls (see Figure FP-2.6).
Correlations between the RLC and LC groups of figure FP-2.3 and the DF biquad functions yield:
(a)
Q = L1z / R1x
where
L1z = L1x / BW
(FP2-1)
where L 2 z = C 2 x * BW
(FP2-2)
(and L1x = table value and R1x = 1.0Ω)
(b)
k1 = 1 /(2 * Q * L 2 z )
(and C2x = table value)
(c)
k 2 = (Q / C 2 z ) /(1 + 2 * Q * Q)
where C 2 z = C 2 x / BW
(FP2-3)
since (in this case) L3z = L1z
(FP2-4)
(and C2x = table value)
(d)
k 3 = 1 /(2 * Q * L3z ) = k1
So your ‘pSPICE ready’ completed form will look like
Figure FP-2.6: ‘pSPICE ready’ circuit for the bandpass 3rd –order profile, leapfrog realization. Note
that the relationships are defined entirely in terms of parameter specifications (the lists of parameters
below the circuit), The first set of parameters are the same as those for Figure FP-2.4, except with the
relationships of equations (FP2-1), (FP2-2), (FP2-3), and (FP2-4) applied. The second set of
parameters is the LP:BP conversion. The third set of parameters is a copy/paste of those used in
figure FP2-3.
Your mission, should you choose to accept it, is to develop a 3rd-order 0.5dB Chebyshev profile
centered at f0 = 20kHz with BW = 5kHz.
1. Using the techniques and examples identified by the professor notes, section 24.6 and example
24.6-10, execute simulations using a VAC source of amplitude 1.0V, for each of the following and
frequency sweep range of 0.1 f0 to 10 f0.
(a) Figure FP-2.3 (above) for the normalized 3rd-order 0.5dB doubly-terminated Chebyshev
RLC ladder with ω0 =1.0r/s and BW = 0.25 (consistent with mission target).
Make a snapshot (10pts) of your schematic as your figure 11.1a.
(10 pts) Execute the simulation and overlay plots of amplitude |T| and phase P( ) (Note: be
sure to call up a new Y-axis for the P( ) plot). Mark the low and high break points with your cursor
(separately for each plot). Make snapshot of the plot (including cursor coordinates) as your figure
11.1b. You should also confirm that center frequency ω0 = 1.0r/s (same as f0 = 160mHz).
(b) Realize the leapfrog form of this BP circuit, either as represented by figure 24.6-9 from
professor notes, section 24.6 or from figure FP-2.5 (above). Assemble in the same manner as
indicated by the FP-2.1 thru FP-2.5 method above in order to minimize topology errors.
Make a snapshot (10 pts) of your schematic as your figure 11.2a.
(10 pts) Mark the low and high break points on this circuit with your cursor and make
snapshots (including cursor coordinates) of the amplitude |T| profile (only) as your figure 11.2b. You
should also confirm that center frequency ω0 = 1.0r/s (same as f0 = 160mHz). If the result is not the
same as for the RLC circuit form, make a snake check. Your figures 11.1b and 11.2b should come
out to be nearly identical.
2. (20 pts) Now execute a frequency rescale which implements this circuit at 20 kHz (and BW = 5
kHz) for an equal-capacitance form for which all capacitances = 330pF. Note that you can do this
parametrically using pSPICE, since you have specified all of the R’s and C’s in step 1 (a) and (b) at
the normalized frequency ω0 = 1.0r/s. It is suggested that each component be given a scaling factor,
applied to its value. The scaling factor should be according to type, i.e. sC for capacitances and sR
for resistances. In many instances these scaling factors can be inserted into the PARAMETER tables
(but not for all component values).
Make a snapshot of your schematic as your figure 11.3a.
(a) (10pts) Produce a plot of |T| for sweep range 0.1 f0 to 10 f0 with the low and high break
points marked with your cursor Snapshot this figure as your figure 11.3b (cursor coordinates
included).
(b) (10 pts) Reset the trace to dB(ABS(Vout/Vin)) and (with your cursors) measure the
passband ripple (using your cursors). Snapshot this figure ((including cursor coordinates) as your
figure 11.3c. Your passband ripple should be on the order of 0.5dB, since that’s what you have
speficifed by choice of the 0.5dB Chebyshev.
(c) (10 pts) Reset the trace to show the roll-off (in dB/decade) using the PROBE ‘macro’
D(DB(ABS(V(v2)/10mV)))/ D(LOG(Frequency)),
and (with your cursors) identify the maximum roll-off in dB/decade and the roll-off (in dB/dec) for f
>> f0 . Snapshot this figure as your figure 11.3d (including cursor coordinates). Comment on the
results.
3. (10 pts) Execute a 5-pass Monte-Carlo analysis with tolerance on all components of 5% and
display results. Show a snapshot of your results as your figure 11.4, and identify the variation in
break frequency f0 and the BW (in Hz) that results using your cursor to make measurements. Indicate
your results in a short table.