Low-Sensitivity, Highpass Filter Design With Parasitic Compensation
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Low-Sensitivity, Highpass Filter Design With Parasitic Compensation
Kumen Blake
October 1996
Introduction This Application Note covers design Sallen-Key highpass biquad. This design gives component sensitivities. also shows compensate amp's bandwidth (pre-distortion) parasitic capacitances. design example illustrates this method. These biquads also called VCVS [voltagecontrolled, voltage-source]. Changes component values over process, environment time affect performance filter. achieve greater production yield, filter needs insensitive these changes. This Application Note presents design algorithm that results sensitivity component variation. information evaluating sensitivity performance your filter. achieve best production yield, nominal filter design must also compensate component board parasitics. components pre-distorted compensate bandwidth. This Application Note expands pre-distortion method include compensation parasitic capacitances. This method valid either voltage-feedback current-feedback amps. Parasitic Compensation pre-distort your filter components compensate parasitic capacitances: method include amp's effect filter response. result transfer function same order whose coefficients include group delay (oa) evaluated passband edge frequency (fc). parasitic capacitances parallel with capacitors: capacitors together Simplify resulting coefficients time constants form coefficients when possible parasitic capacitances parallel with resistors: Replace resistor filter transfer function with parallel equivalent
create terms coefficient times
power transfer function after simplifying most useful approximations are:
RxCps)
These approximations valid when:
(RxCp
Convert RxCps) exponential form
pure time delay) when multiplies, divides, entire transfer function change gain allpass sections When simplifying, discard terms that products error terms (Koa RxCp); they negligible time constants form coefficients when possible with adequate bandwidth (f3dB) slew rate (SR): f3dB 10fH 5fHVpeak where highest frequency passband filter, Vpeak largest peak voltage. This increases accuracy pre-distortion algorithm. also reduces filter's sensitivity performance changes over temperature process. Make sure stable gain Highpass Biquad Design biquad shown Figure Sallen-Key highpass biquad. needs voltage source with output impedance. transfer function
simplify:
Alter this impedance convenient form
1996 National Semiconductor Corporation
Printed U.S.A.
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where:
Initialize resistance level Increasing will:
Increase output noise Reduce distortion Improve isolation between Make parasitic capacitances larger fraction
Initialize capacitance level C1C3 component ratios outputs
5C1C3
0.10 0.10,
Figure Highpass Biquad achieve sensitivities, this design algorithm: Partition gain good sensitivity dynamic range performance: noise amplifier before this biquad need large gain Select with this empirical formula: These values also reduce band width's impact filter response. This biquad's sensitivities high when Select with adequate bandwidth (f3dB) slew rate (SR): f3dB f3dB 10fc 5fHVpeak where highest signal frequency, corner frequency filter, Vpeak largest peak voltage. Make sure stable gain current-feedback amps, recommended value gain voltage-feedback amps, select noise distortion performance. Then correct gain:
Recalculate initialize capacitors:
nearest standard values. Recalculate C1C3
Calculate resistors:
component sensitivity formulas table below. sensitivities measure this biquad's sensitivity group delay [5]. evaluate this sensitivity performance, method [6].
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(p(pd)C)
4Qp(pd) Qp(pd)
Calculate resulting parasitic correction factors: 4Cni Calculate resulting filter response parameters p(pd)
p(pd)
Highpass Biquad Parasitic Compensation pre-distort this biquad, compensate [parasitic] non-inverting input capacitance (Cni), following (see Appendix derivation formulas): Start iterations ignoring parasitics: Estimate pre-distorted values (p(pd) Qp(pd)) that will compensate Cni: p(pd) p(nom)
p(nom)
Qp(pd) Qp(pd) p(pd)
Repeat steps until: p(nom) Qp(nom)
Estimate high frequency gain:
2p(pd)
Qp(pd) Qp(nom) p(pd) Qp(nom) p(pd) p(nom) where p(nom) Qp(nom) nominal values Recalculate resistors capacitors using p(pd) Qp(pd):
p(pd)
this reduces gain much, then repartition gain. Design Example circuit shown Figure 3rd-order Butterworth highpass filter. Section buffered single pole section, Section highpass biquad. voltage source with output impedance, such CLC111 buffer, Vin. nominal filter specifications are:
5C1C3
(p(pd)Qp(pd)
Design Example accomplishes this recalculating then
50MHz 10MHz 200MHz 3.0dB 40dB
(passband edge frequency) (stopband edge frequency) (highest signal frequency) (maximum passband ripple) (minimum stopband attenuation) (passband voltage gain)
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Figure Highpass Filter 3rd-order Butterworth filter [1-4] meets specifications. pole frequencies quality factors are: Section [MHz] 50.00 50.00 1.000
Section Design: Since Qp=1.000, 1.00 CLC446. This current-feedback f3dB 400MHz 200MHz f3dB 10fc 500MHz; design will sensitive group delay 2000V/µs 1000V/µs (see Item "Section Design") 0.56ns 10MHz Cni(446) 1.0pF (input capacitance) CLC446's recommended 1.0: Then leave open that 1.00 Initialize resistor level: Initialize capacitor level, component ratios: 31.83pF (50.00MHz) (100) 0.1000 {0.10,0.0826} 0.1000 Recalculate initialize capacitors: 0.127 89.3pF 11.3pF capacitors nearest standard values: 91pF 11pF Recalculate capacitor level ratio, resistor level ratio: Calculate resistors: 31.2
Overall Design: Restrict resistor capacitor ratios resistors (chip metal film, 1206 SMD) capacitors (ceramic chip, 1206 SMD) standard resistor capacitor values Section Design Pre-distortion: CLC111. This closed-loop buffer. f3dB 800MHz 200MHz f3dB 800MHz 10fc 500MHz 3500V/µs, while 200MHz, 2Vpp sinusoid requires more than 1000V/µs 0.28ns 10MHz Cni(111) 1.3pF (input capacitance) Select noise, distortion properly isolate CLC111's output C1A. predistorted value R2A, that also compensates Cni(111), [5]:
sensitivities this design are:
(91pF) (11pF) 31.64pF (11pF) 0.1209 (91pF)
(C1A Cni(111)
(50.00MHz) (31.64pF)
results table below: Initial Value column shows ideal values that ignore parasitic effects Adjusted Value column shows component values that compensate Cni(111) group delay (oa) Standard Value column shows nearest standard resistors capacitors
Component
100.6 0.1056
0.00 0.00 0.00 0.00 0.00 0.00 1.00
-0.50 -0.50 -0.50 -0.50 0.00 0.00 0.00
-0.39 0.39 0.50 -0.50 0.00 0.00 1.12
Initial 30pF
Value Adjusted 30pF 92.8 1.3pF
Standard 30pF 93.1 1.3pF
Cni(111)
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Section Pre-distortion: design gives these values: p(nom) 2(50.00MHz) Qp(nom) 1.000 1.00 91pF 11pF Iteration shows initial design results. Iterations pre-distort compensate CLC446's group delay, Cni(446): 59.73 0.9320 84.22 0.1108 253.0 28.03 0.253 1.511 51.96 0.984 56.81 0.9561 88.54 0.1053 272.9 28.73 0.273 1.575 49.52 1.003 57.54 0.9505 87.42 0.1065 267.9 28.53 0.268 1.559 50.13 0.999 Figure Simulated Filter Magnitude Response SPICE Models SPICE models available most Comlinear's amplifiers. These models support nominal noise transient simulations room temperature. recommend simulating with Comlinear's SPICE models Predict amp's influence filter response Support quicker design cycles Include board component parasitic models obtain more accurate prediction filter's response. verify your simulations, recommend bread-boarding your circuit. Summary This Application Note contains easy design algorithm sensitivity, Sallen-Key highpass biquad. Designing sensitivities gives: Figure Simulated Filter Magnitude Response
Iteration p(pd) [MHz] 50.00 Qp(pd) 1.000 100.6 0.0962 324.3 31.21 [ns] 0.324 [ns] 1.741 [MHz] 43.87 1.034
midband gain estimate 0.770 [V/V]. Iteration 0.759 [V/V]. Iteration simulations gave lower value Increasing could help overcome this loss, would also increase sensitivities. resulting components are: Value Adjusted 91pF 11pF 1.0pF 28.5
Component
Initial 91pF 11pF 31.2
Standard 91pF 11pF 1.0pF 28.7
Cni(446)
Reduced filter variation over process,
temperature time
Figures show simulated gains. curve numbers are: Ideal (Initial Design Values, Without pre-distortion (Initial Design Values, With pre-distortion (Pre-distorted Values,
Higher manufacturing yield Lower component cost
sensitivity design enough produce high manufacturing yields. This Application Note shows compensate bandwidth, [parasitic] input capacitance amp. This method also applies other component board parasitics. components must also have enough tolerance temperature coefficients.
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Appendix Derivation Pre-distortion Parasitic Capacitance Compensation Formulas pre-distort this filter, compensate [parasitic] input capacitance (Cni): method include amp's effect filter response. result
After simplifying, obtain:
where
where group delay (oa) evaluated passband edge frequency (fc), and:
4Cni
5C1C3 )Cni
5C1C3
Since parallel with replace with parallel equivalent Cni: 4Cnis) 4Cnis
(R5C1 4Cnis
Appendix Bibliography Schaumann, Ghausi Laker, Design Analog Filters: Passive, Active Switched Capacitor. Jersey: Prentice Hall, 1990. Zverev, Handbook FILTER SYNTHESIS. John Wiley Sons, 1967. Williams Taylor, Electronic Filter Design Handbook. McGraw Hill, 1995. Natarajan, Theory Design Linear Active Networks. Macmillan, 1987. Blake, "Component Pre-distortion Sallen-Key Filters," Comlinear Application Note, OA-21, Rev. July 1996. Blake, "Low-Sensitivity, Lowpass Filter Design," Comlinear Application Note, OA-27, July 1996. Blake, "Low-Sensitivity, Bandpass Filter Design With Tuning Method, "Comlinear Application Note, OA-28, Oct. 1996.
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