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Analog and Telecommunication Electronics
E1 - Filters type and design» Taxonomy and parameters» Design flow and tools » FilterCAD example» Basic II order cells
AY 2015-16
Politecnico di TorinoElectronic Eng. Master Degree
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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 …: 3, 4.1 Active Filters– Elettronica per Telecom.: 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(betweenantenna and RX/TX amplifiers): tuned circuits(LC) or mechanical(ceramicresonators)
IF channel filters (narrowband-pass), isolate single radio channels). Same technologies as RF
Baseband and audio filters (low-pass). Active filters
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Filter types and parameters
• Function of a filter:– Get a defined frequency response
H(ω) = Vo/Vi
• Transfer function type
– High-pass
– Low-pass
– Band-pass/reject
• Lin/log representation
ω
H(ω)Vi Vo
H(ω)
H(ω)
H(ω)
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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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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 TuningPole number 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 domainstep 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 =
R3 =
R4 =
C2 =
C5 =
Evaluate
n = ?
= ?
H(0) = ?
R3
AOVI
-
+ VU
C5R1
R4
C2
A
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Example circuit: frequency response
Bode plot (on the web: Simulators, II order functions, or SPICE analysis)
R3
AO
VI
-
+ VU
C5R1
R4
C2
A
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Example circuit: time-domain response
Step response (on the web: Simulators, II order functions, or SPICE analysis)
R3
AO
VI
-
+ VU
C5R1
R4
C2
A
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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 circuitprovideslow/band/high-pass
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Comparison with LTC1562 cell
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
I1
I2
I1I2
A
A
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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 ofschematic(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.