ATLCE - E1
06/05/2016
Politecnico di Torino
Electronic Eng. Master Degree
Analog and Telecommunication
Electronics
E1 - Filters type and design
»
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Taxonomy and parameters
Design flow and tools
FilterCAD example
Basic II order cells
AY 2015-16
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Lesson E1: Filters type and design
• Filter taxonomy and parameters
• Design flow
• Design tools
– FilterCAD example
• Basic II order cells with Op Amp
– Multiple feedback
– Finite gain
– Two-integrator loop
• References:
– Design with Op Amp …:
– Elettronica per Telecom.:
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3, 4.1 Active Filters
2.1.3 Filtri attivi
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Goals of this lesson
• Understanding of filter types and parameters
– Low-pass, high-pass, band-pass/reject
• Knowledge of technologies to build filters (not RF)
– Passive, active Op Amp, Switched Capacitor
• Use of CAD tools for filter design
– Filter design process
• Knowledge of Op Amp circuits for basic cells
• Ability to design II order cells with Op Amps
– Finite gain, multiple, feedback, …
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Many types of filters
RF filters
(between
antenna and
RX/TX
amplifiers):
tuned circuits
(LC) or
mechanical
(ceramic
resonators)
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IF channel filters (narrow
band-pass), isolate single
radio channels).
Same technologies as RF
Baseband and
audio filters (lowpass).
Active filters
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Filter types and parameters
• Function of a filter:
– Get a defined frequency response
Vi
H(ω)
Vo
H(ω) = Vo/Vi
• Transfer function type
– High-pass
H(ω)
ω
– Low-pass
H(ω)

– Band-pass/reject
H(ω)

• Lin/log representation
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Filter examples - a
• Pass-band
– Radio Frequency (GHz)
» Remove outband signals for RX
» Reduce harmonics and distortion for TX
» Based on tuned circuits

– Intermediate frequency channel
» Isolate single channels
» Based on LC or mechanical resonators, or digital processing
• Low-pass
– Anti-aliasing before ADC, reconstruction after DAC
» Active filters with R, C, Op Amp
» Switched Capacitor circuits

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Filter examples - b
• High pass
– Remove DC (or LF) from the signal
» Cancel offset and other DC errors
» R, C, Op Amp, SC

• Band reject
– Remove specific interferences
» Low frequency (50/60 Hz)
R, C, Op Amp, SC
» EMC/Radio interferers

• Notch filters
– Remove a single F
» Tuned circuits
» Mechanical filters
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
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Structure of filters (low-pass)
• We can get only
approximation of ideal H(ω)
– Causality principle
» Hard F limit  infinite in time
– Tolerances
» Real value of devices
• Any p(s) with real coefficients
can be decomposed in I and
II order terms, with real
coefficients.
– Any p(s) can be built with a
cascade of I or II order cells
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Filters: design sequence
• Define specifications (filter mask)
» Band-pass gain and ripple
» Cutoff frequency and slope
» Band-reject attenuation
• Filter design
» Which approximation?
» How many cells?
• Selection of technology
» Analog/digital?
» Which circuit for basic cells?
• Circuit design
» schematic diagram, values of components, tolerances, …
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Filter technologies
• Analog filters:
– Passive LC (R): inductors, capacitor, (resistors)
» Size, weight, parasitic
– Active filters (Op Amps + RC)
» Active device constraints (need power, limited range, …)
– SC (Switched Capacitors)
» Most common technique in current ICs
• Digital filters (not addressed in this course):
– Need A/D and D/A conversion
» Intrinsic aliasing & quantization errors
» Need processing power, memory, …
– Mostly automated design
– Digital processing with microP, DSP, FPGA (easy to modify)
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Filters: approximation types
• Ideal transfer funct. approximated as polynomials ratio
• Several choices for approximation, such as:
– Bessel
» Linear phase, no ripple in passband
» Least steep
– Butterworth
» No ripple in passband
– Chebicheff
» Ripple in passband
» Most steep around cutoff
– …. Many others, with different optimizations
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Bessel approximation
– Linear phase, constant group delay, no distortion
– No ripple in pass-band
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Butterworth approximation
– No ripple in pass-band
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Chebicheff approximation
– Ripple
– Very steep
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Cell parameters
• Each cell has a II order response
• ω0 and ξ cannot be directly measured
– Design from ω0 and ξ
– Test and tuning from peak position (ωα) and amplitude
Design
Pole
number
Tuning
cell
real pole
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Filter design tools
• Several deign tools availble on the web
• Linear Technology:
http://ltspice.linear.com/software/FilterCAD.zip
(simple)
• Texas Instruments:
http://www.ti.com/lsds/ti/analog/webench/webench-filters.page
(complete)
• Others ….
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Filter design: example 1 - a
• Specs definition, or filter mask
–
–
–
–
–
Passband gain
Passband ripple (R)
Stopband attenuation (A)
Passband limit (Fc)
Stopband limit (Fs)
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Filter design: example 1 - b
• Design of the filter
– Which approximation?
– How many poles/cells needed?
– Which parameters for each cell?
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Filter design: example 1 - c
• Frequency
response
time domain
step
response
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Filter design: example 1 - d
• Select technology
– Switched capacitor or R + C + A.O. (active RC) ?
– Which basic cell circuit?
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II order cells
• The basic II order cell can use:
– L, C, (R) – actually used only for RF
– Specific IC, with internal Op Amps (e.g. the LTC1562)
• Op Amp with feedback (R, C)
– Multiple feedback, Constant gain, Double integrator, …
– Critical issue: tolerances
» Need high precision passive components (R, C)
» OK for “discrete”, difficult to get inside ICs
• Switched Capacitor circuits far better for integration
– High precision ratio of the same component (C)
– General trend to use SC to replace R
» Filters, amplifiers, ADC/DAC, …
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II order cell with Op Amp: example 1
A
vA
Can be low/high/band pass,
depending on choices of Yi
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Example circuit: low-pass cell analysis
R1 =
R4
R1
R3 =
R4 =
C2 =
R3
A
VI
C5
C2
+
AO
VU
C5 =
Evaluate
n = ?
 =?
H(0) = ?
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Example circuit: frequency response
R4
R1
Bode plot
(on the web: Simulators, II order functions,
or SPICE analysis)
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VI
R3
C5
-
A
C2
+
AO
VU
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Example circuit: time-domain response
R4
R1
Step response
(on the web: Simulators, II order functions,
or SPICE analysis)
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VI
R3
C5
-
A
C2
+
AO
VU
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II order cell with Op Amp: example 2
• Finite gain (K) circuit
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II order cell with Op Amp: example 3
2-integrator cell
Same circuit
provides
low/band/high-pass
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Comparison with LTC1562 cell
A
I2
I2
I1
I1
A
The LTC 1562 cell is actually a two-integrator loop.
The adder A uses the inverting input of the Op Amp (integrator 1)
Complete data sheet: http://www.linear.com/pdf/1562fa.pdf
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Basic cell of LTC1562 filter IC
4 double integrator cells
Parameters defined by
external components
Data sheet: http://www.linear.com/pdf/1562fa.pdf
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Filter design: example 1 - e
• Final complete circuit diagram (from FilterCAD)
Not the best
type of
schematic
(topographic/
functional)
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Lesson E1: Final test
• Describe filter taxonomy, based on frequency response.
• Which are the parameters that define a filter?
• For one of tf the filter types, describe the effect of changing the
frequency response parameters on the time-domain step
response.
• Describe the design flow for a filter.
• Which are the benefits and drawbacks of active filters built with
Op Amps?
• Describe at least two circuits to get II order response from RC
circuits.
• Draw he diagram of a Multiple Feedback low-pass cell.
• Draw the diagram of a Finite Gain low-pass cell.
• Turn the cell into high-pass.
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