DESIGN THE ANALOG FILTER FOR THE SCENARIO.(Sample Task)
Consider the case of detection of human breathing and heartbeat by short range radar signals. The
signals reflected from a human subject show nearly periodic modulation signals in the range of
(i)
(ii)
0.8Hz-2.5Hz for heartbeat, and
(ii) 0.2Hz-0.5Hz for breathing
It is required to isolate the above signals in a signal processing scenario. The work can be
accomplished by two band-pass filters with an isolation of at least 40dB between the band-edges of
the breathing (i.e., 0.5Hz) and the heartbeat (i.e. 0.8Hz) signals.
Consider the band-pass filter for detecting the breathing signal with equi-ripple passband
characteristic.
1. Synthesize the filter transfer function (it will be of order >2).
2. Provide a decomposition of the transfer function as cascade of second order and possibly first
order transfer functions.
3. Verify that the transfer function obtained satisfy the given specification (use numerical
simulation, i.e., MATLAB).
Use a frequency scaling (scale upward) by 1000 to the above filter function. Then perform the
following tasks with the new transfer function.
4. Provide a design1 for the above filter, using
(a) Passive L,C,R ladder sections with equal termination of R =100 ohms.
(b) OTA based active filter.
The OTAs could be deployed to implement the L elements in 4(a). You can use the VCCS module
from the SPICE library for the OTA.
5. From the work in step 2 above, use one of the second order transfer functions for the following
tasks.
(a) Produce a design of the second order filter using OA. Use of nearest practical values of R,C
elements (as obtained from the lab bins, i.e., for R= 1.231 kΩ, use 1.2 kΩ, and for C=0.125 µF. use 0.1
µF, or 0.1 µF plus 20 nF in parallel) is encouraged.
• Provide SPICE simulation results and a comparison with the theoretical transfer function
(second order). The theoretical transfer function can be obtained using numerical simulation (i.e.,
MATLAB). Use model of a practical OA such as µ741 from the SPICE data base.
(b) Produce a design of the second order filter using CCII (equivalent circuit model) and capacitors.
Use of nearest practical values for the C elements (as obtained from the lab bins, i.e., for C=0.125 µF.
use 0.1 µF, or 0.1 µF plus 20 nF in parallel) is encouraged. Provide SPICE simulation results and a
comparison with the theoretical transfer function (second order). The theoretical transfer function
can be obtained using numerical simulation (i.e., MATLAB).