818 Series 1 kHz to 1.28 MHz 8-Bit Programmable 2" x 4" 8-Pole Filters Description The 818 Series are digitally programmable low-pass and high-pass active filters that are tunable over a 256:1 frequency range. 818 filters are available with any one of five standard factory-set tuning ranges or 8-bit custom ranges from 1 kHz to 1.28 MHz. These units contain 8 CMOS logic inputs. 818 Series models are convenient, low profile, easy to use fully finished filters which require no external components or adjustments. They feature low harmonic distortion, and near theoretical amplitude characteristics. 818 filters operate from non-critical ±12 to ±18 Vdc power supplies, have a 5 kΩ (min.) input impedance, a 10Ω (max.) output impedance and low-pass models offer dc voltage offset adjustment. Features/Benefits: • Low harmonic distortion and wide signal-to-noise ratio to 12-bit resolution • Digitally programmable corner frequency allows selecting cut-off frequencies specific to each application • Plug-in ready-to-use, reducing engineering design and manufacturing cycle time • Factory-set tuning range, no external clocks or adjustments needed • Broad range of transfer characteristics and corner frequencies to meet a wide range of applications Programmable Specifications. . . . . . . . . . . . . . Page Digital Tuning & Control . . . . . . . . . . . . . . . . . . . . . . 2 Available Low-Pass Models: . . . . . . . . . . . . . . . Page 818L8B 8-pole Butterworth . . . . . . . . . . . . . . . . . . 3 818L8L 8-pole Bessel . . . . . . . . . . . . . . . . . . . . . . 3 818L8E 8-pole, 6-zero elliptic, 1.77 . . . . . . . . . . . . 3 818L8D80 8-pole, 6-zero constant delay . . . . . . . . . . 3 Applications • Anti-alias and band-pass filtering • Data acquisition systems • Satellite and telecommunications • Acoustic and vibration analysis and control • Aerospace, navigation and sonar Available High-Pass Models: . . . . . . . . . . . . . . Page 818H8B 8-pole Butterworth . . . . . . . . . . . . . . . . . . 4 818H8E 8-pole, 6-zero elliptic, 1.77 . . . . . . . . . . . . 4 General Specifications: Phase and phase match considerations . . . . . . . 5 & 6 Ordering information . . . . . . . . . . . . . . . . . . . . . . . . . 7 Pin-out/package data. . . . . . . . . . . . . . . . . . . . . . . . . 7 • Medical research and electronic equipment • Engine test and simulation • Noise elimination • Video systems • Signal reconstruction 25 Locust St, Haverhill, Massachusetts 01830 • Tel: 800/252-7074, 978/374-0761 • FAX: 978/521-1839 e-mail: [email protected] • Web Address: http://www.freqdev.com 818 Series Digital Tuning & Control Characteristics 8-Bit Programmable Filters Digital Tuning Characteristics Pin-Out Key The digital tuning interface circuits are two 4042 quad CMOS latches which accept the following CMOS-compatible inputs: eight tuning bits (D0 - D7), a latch strobe bit (C), and a transition polarity bit (P). IN OUT GND "P" "C" +Vs -Vs Os NC Filter tuning follows the tuning equation given below: 7 6 5 4 fc = ( fmax/256 ) [ 1 + D7 x 2 + D6 x 2 + D5 x 2 + D4 x 2 + D3 x 3 2 1 0 2 + D2 x 2 + D1 x 2 + D0 x 2 ] where D1 - D7 = "0" or "1", and fmax = Maximum tuning frequency; fc = corner frequency; Minimum tunable frequency = fmax/256 (D0 thru D7 = 0); Minimum frequency step (Resolution) = fmax/256 Analog Input Signal Analog Output Signal Power and Signal Return Transition Polarity Bit Tuning Strobe Bit Supply Voltage, Positive Supply Voltage, Negative Optional Offset Adjustment No Connect (Highpass Models) D7 Tuning D6 Tuning D5 Tuning D4 Tuning D3 Tuning D2 Tuning D1 Tuning D0 Tuning Bit Bit Bit Bit Bit Bit Bit Bit 7 (MSB) 6 5 4 3 2 1 0 (LSB) OUT +Vs -Vs D7 D6 D5 D4 Data Control Specifications GND Data Control Lines Functions D2 Data Control Modes Mode 1 Mode 2 Input Data Levels D3 IN Os/NC P = 1; C = 1 frequency follows input codes P = 1; C = 1⇓ frequency latched on falling edge (CMOS Logic) 4 Vdc max. 15 Vdc max. Input Current High Level In Low Level In - 10 µA typ. -5 +10 µA typ. -1 mA max. +1 µA max. 5 pF typ 7.5 pF max. Input Data Format Positive Logic Bit Weighting D0 D7 Frequency Range D0 P C Bottom View P = 0; C = 0 frequency follows input codes P = 0; C = 0⇑ frequency latched on rising edge Input Voltage (Vs = 15 Vdc) Low Level In 0 Vdc min. High Level In 11 Vdc min. Input Capacitance Latch Response 1 Data Set Up Time 2 Data Hold Time Strobe Pulse Width D1 Latch Strobe (C) Transition Polarity (P) -5 25 nS 50 nS 80 nS min. Frequency Select Bits Logic "1" = +Vs Logic "0" = Gnd (Binary-Coded) LSB (least significant bit) MSB (most significant bit) 256 : 1, Binary Weighted Bit Weight MSB --- --- --- --- --- --- LSB 27 26 25 24 23 22 21 20 fc D7 D6 D5 D4 D3 D2 D1 D0 Corner Frequency 0 0 0 0 0 0 0 0 fmax/256 0 0 0 0 0 0 0 1 fmax/128 0 0 0 0 0 0 1 1 fmax/64 0 0 0 0 0 1 1 1 fmax/32 0 0 0 0 1 1 1 1 fmax/16 0 0 0 1 1 1 1 1 fmax/8 0 0 1 1 1 1 1 1 fmax/4 0 1 1 1 1 1 1 1 fmax/2 1 1 1 1 1 1 1 1 fmax Notes: 1.Frequency data must be present before occurrence of strobe edge. 2.Frequency data must be present after occurrence of strobe edge. 2 25 Locust St, Haverhill, Massachusetts 01830 • Tel: 800/252-7074, 978/374-0761 • FAX: 978/521-1839 e-mail: [email protected] • Web Address: http://www.freqdev.com 818 Series 8-Pole Low-Pass Filters 8-Bit Programmable Model 818L8B 818L8L 818L8E 818L8D80 Transfer Function 8-Pole, Butterworth 8-Pole, Bessel 8-Pole, 6 zero, Elliptic 8-Pole, 6 zero, Constant Delay Size 2.0” x 4.0” x 0.4” 2.0” x 4.0” x 0.4” 2.0” x 4.0” x 0.4” 2.0” x 4.0” x 0.4” Range fc 1 kHz to 128 MHz 1 kHz to 1.28 MHz 1 kHz to 1.28 MHz 1 kHz to 1.28 MHz Theoretical Transfer Characteristics Appendix A Page 9 Appendix A Page 4 Appendix A Page 24 Appendix A Page 21 Passband Ripple 0.0 dB 0.0 dB ± 0.035 dB 0.15 dB 0 ± 0.1 dB max. 0 ± 0.05 dB typ. 0 ± 0.1 dB max. 0 ± 0.05 dB typ. 0 ± 0.1 dB max. 0 ± 0.05 dB typ. 0 ± 0.1 dB max. 0 ± 0.05 dB typ. Stopband Attenuation Rate 48 dB/octave 48 dB/octave 80 dB min. 80 dB min. Cutoff Frequency Stability Amplitude Phase fc ± 0.01% /°C - 3 dB -360° Filter Attenuation 0.12 dB 3.01 dB 60.0 dB 80.0 dB Product Specifications (theoretical) DC Voltage Gain (non-inverting) (theoretical) ± 3% max. 0.80 fc 1.00 fc 2.37 fc 3.16 fc fc ± 0.01% /°C - 3 dB -182° ± 3% max. 1.91 dB 3.01 dB 60.0 dB 80.0 dB 0.80 fc 1.00 fc 4.52 fc 6.07 fc fr ± 0.01% /°C - 0.035 dB - 323.5° ± 3% max. 0.035 dB 3.01 dB 60.0 dB 80.0 dB 1.00 fr 1.13 fr 1.67 fr 1.77 fr fc ± 0.01% /°C - 3 dB -306° ± 3% max. 3.01 dB 60.0 dB 80.0 dB 1.00 fc 3.08 fc 3.57 fc Phase Match1 See page 5 & 6 See page 5 & 6 See page 5 & 6 See page 5 & 6 Amplitude Accuracy 0 - 0.6 fc ± 0.5 dB max. ± 0.25 dB typ. 0.6 fc - 1.0 fc ± 1.0 dB max. ± 0.6 dB typ. 0 - fc 0 - 0.8 fr ± 0.5 dB max. ± 0.25 dB typ. 0.8 fc - 1.0 fr ± 1.0 dB max. ± 0.5 dB typ. 0 - 0.8 fc Total Harmonic Distortion @ 1 kHz < - 88 dB typ. < - 88 dB typ. < - 88 dB typ. < - 88 dB typ. Wide Band Noise 300 µVrms typ. 300 µVrms typ. 350 µVrms typ. 300 µVrms typ. 75 µVrms typ. 75 µVrms typ. 75 µVrms typ. 75 µVrms typ. FMA-04A FMA-04A FMA-04A FMA-04A (theoretical) ± 0.8 dB max. ± 0.4 dB typ. 0.8 fc - 1.0 fc ± 0.5 dB max. ± 0.25 dB typ. ± 1.0 dB max. ± 0.5 dB typ. (5 Hz - 2 MHz) Narrow Band Noise (5 Hz - 100 kHz) Filter Mounting Assembly 1.Unit to unit match for the same transfer function, set to the same frequency and operating configuration, and from the same manufacturing lot. 3 25 Locust St, Haverhill, Massachusetts 01830 • Tel: 800/252-7074, 978/374-0761 • FAX: 978/521-1839 e-mail: [email protected] • Web Address: http://www.freqdev.com 818 Series 8-Pole High-Pass Filters 8-Bit Programmable Model 818H8B 818H8E Transfer Function 8-Pole, Butterworth 8-Pole, 6-zero, Elliptic Size 2.0” x 4.0” x 0.4” 2.0” x 4.0” x 0.4” Range fc 1 kHz to 1.28 MHz 1 kHz to 1.28 MHz Theoretical Transfer Characteristics Appendix A Page 29 Appendix A Page 37 Passband Ripple 0.0 dB ± 0.035 dB 0 ± 0.5 dB to 1.28 MHz 0 ± 0.5 dB to 1.28 MHz Power Bandwidth (-6 dB) 5 MHz (-6 dB) 5 MHz Stopband Attenuation Rate 48 dB/octave 80 dB Cutoff Frequency Stability Amplitude Phase fc ± 0.01% /°C - 3 dB -360° Filter Attenuation 80 dB 60 dB 3.01 dB 0.00 dB Product Specifications (theoretical) Voltage Gain (non-inverting) (theoretical) Amplitude Accuracy ± 3% max. 0.31 fc 0.42 fc 1.00 fc 2.00 fc fr ± 0.01% /°C - 0.035 dB -323.5° ± 3% max. 80.0 dB 60.0 dB 3.01 dB 0.03 dB 00.0 dB 0.56 fr 0.60 fr 0.88 fr 1.00 fr 2.00 fr 1.0 - 1.25 fc ± 0.5 dB max. ± 0.3 dB typ. 1.25fc-1.28MHz± 1.0 dB max. ± 0.5 dB typ. 1.00 - 1.25 fr ± 0.5 dB max. ± 0.3 dB typ. 1.25fr-1.28MHz± 1.0 dB max. ± 0.5 dB typ. Total Harmonic Distortion @ 1 kHz < - 88 dB typ. < - 88 dB typ. Wide Band Noise 400 µVrms typ. 450 µVrms typ. Narrow Band Noise 100 µVrms typ. 100 µVrms typ. Filter Mounting Assembly FMA-04A FMA-04A (theoretical) 1.Unit to unit match for the same transfer function, set to the same frequency and operating configuration, and from the same manufacturing lot. 4 25 Locust St, Haverhill, Massachusetts 01830 • Tel: 800/252-7074, 978/374-0761 • FAX: 978/521-1839 e-mail: [email protected] • Web Address: http://www.freqdev.com 818 Series Phase and Phases Match Considerations 1 kHz to 1.28 MHz Phase Deviation from Theoretical: EXAMPLE: Phase Match Calculation The phase response of the amplifiers and the capacitance of the frequency control switches of the 818 series contribute to the overall phase response and cause it to deviate from theoretical. For the higher frequency models ( -4 and -5 ), where the cutoff frequencies can be programmed up to 1.28MHz, the deviation from theoretical can be substantial. ∆Φ(f)max = 0.02° x Φτ(f) + 4.0° x f/fc x fmax/1.28MHz 4.0° - L8L 3.0° - L8B & L8D80 2.0° - L8L ∆Φ(f)typ =0.5 x ∆Φ(f)max where: ∆Φ(f) Φτ (f) f f max fc Figure 1 is a normalized plot of the phase deviation from theoretical for an 818L8E-5 for programmed cutoff frequencies from 5kHz ( fc min ) to 1.28MHz (fc max ). For fc of 5kHz, the deviation from the 323° theoretical phase shift is 2° but for fc of 1.28MHz the deviation is 78°. This set of curves can be used to estimate the deviation from theoretical phase for other models in the 818 series. = = = = = phase match at frequency f theoretical phase shift at f frequency of interest maximum fc of the model frequency to which the filter is programmed Eg. - for an 818L8E-3, the phase deviation from theoretical at a frequency of 192kHz, when the cutoff frequency fc is programmed to 384kHz is: Figure 1 represents a "maximum deviation from theoretical phase" situation. Other models (i.e. -1 to -4) will exhibit a similar set of phase deviation curves with the phase scale being reduced by the ratio of the f max of the model to the f max of the -5. For example, an L8E1, whose programming frequency range is from 1kHz to 256kHz (1/5 of the range of the -5 model) will have a similar set of phase deviation curves but the maximum phase deviation, at the highest frequency setting (fc max), will be approximately 1/5 that of the -5 model (78/5 = 15.6°). The other programmed settings of the -1 will also produce proportionally reduced phase deviations. Phase Match: ∆Φ(f)max = 0.02° x Φτ(f) + 4.0° x f/fc x fmax/1.28MHz = 0.02 x (-133°) + 4.0° x 0.5 x 768kHz/1.28MHz = 2.66° + 1.20° = +3.86° Unit to Unit Phase Match2 Theoretical vs. Normalized Input Frequency f/fc = 192kHz/384kHz = 0.5, fmax = 768kHz Φτ(f) = 133° (from data table at f/fc = 0.5) ∆Φ(f)typ =0.5 x ∆Φ(f)max = 0.5° x 3.86° = 1.93° 818L8E Phase Deviation (in degrees “°”) from programmed setting of fc f/fc 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.85 0.90 0.95 1.00 The actual phase shift through a filter at a frequency " f " is determined by its programmed frequency " fc ", the theoretical phase response of the transfer function (B, L, E, or D80) and the phase deviation from theoretical which in turn depends upon component tolerances, the model # (i.e. -1 through -5) and frequency to which it is programmed. It is therefore not possible to have a meaningful unit to unit phase match that is specified by a single number. For a group of the same model type and number, programmed to the same frequency, the unit to unit phase match can be approximated as a percentage of the theoretical phase shift with a correction term added to accommodate amplifier induced phase deviations. 5kHz 0.15 0.30 0.34 0.20 0.20 0.00 -0.21 -0.50 -0.80 -1.20 -1.90 -2.50 10kHz 0.18 0.32 0.42 0.40 0.32 0.00 -0.30 -0.60 -1.00 -1.60 -2.40 -3.30 20kHz 0.17 0.30 0.40 0.50 0.60 -0.10 -0.60 -1.30 -1.80 -2.50 -3.50 -4.60 40kHz 0.08 0.17 -0.18 -0.20 -0.40 -0.80 -1.30 -2.10 -2.80 -3.70 -4.80 -6.20 80kHz -0.12 -0.39 -0.57 -0.90 -1.20 -1.90 -2.70 -3.80 -4.70 -5.80 -7.30 -8.90 160kHz -0.52 -1.03 -1.59 -2.30 -3.00 -4.10 -5.40 -7.20 -8.40 -10.00 -12.00 -14.10 320kHz -1.18 -2.41 -3.66 -5.10 -6.70 -8.70 -11.00 -13.90 -15.80 -18.40 -21.10 -24.30 640kHz 1.28MHz -2.57 -5.32 -5.17 -10.76 -7.89 -16.29 -10.80 -22.10 -14.00 -28.20 -17.70 -35.10 -21.80 -42.60 -26.90 -51.30 -30.10 -56.40 -33.80 -62.30 -38.30 -69.20 -43.30 -77.50 5 25 Locust St, Haverhill, Massachusetts 01830 • Tel: 800/252-7074, 978/374-0761 • FAX: 978/521-1839 e-mail: [email protected] • Web Address: http://www.freqdev.com 818 Series Phase Deviation from Theoretical 5k 10 Hz 20 kH kH z z 10 0 40kHz 80kHz -10 160kHz -20 degrees "°" 320kHz -30 -40 640kHz -50 -60 -70 1.28MHz -80 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 f/fc 6 25 Locust St, Haverhill, Massachusetts 01830 • Tel: 800/252-7074, 978/374-0761 • FAX: 978/521-1839 e-mail: [email protected] • Web Address: http://www.freqdev.com 818 Series Pin-Out and Package Data Ordering Information Specification (25°C and Vs ± 15 Vdc) Analog Input Characteristics1 Impedance Voltage Range Max. Safe Voltage Analog Output Characteristics Impedance (Closed Loop) Linear Operating Range Maximum Current2 Offset Voltage3 Offset Temp. Coeff. Power Supply (±Vs) Rated Voltage Operating Range Maximum Safe Voltage Quiescent Current Pin-Out & Package Data 5 k Ω min. ± 10 Vpeak ±Vs 11 Ω typ. 10 Ω max. ±10V ±5 mA 22 mV typ. 10 mV max. 50 µV/°C 4.00 0.4 0.2 min 0.04 Dia. Side View All dimensions are in inches All Case Dimensions ± 0.02" Grid Dimensions 0.1" x 0.1" OUT +Vs -Vs D7 D6 ±15 Vdc ±12 to ±18 Vdc ±18 Vdc D5 D4 GND 2.00 100 mA typ. 120 mA max. D3 D2 D1 Temperature Operating Storage D0 -20 to +70°C -25 to +85°C 4 IN Os /NC Notes: Bottom View P C Filter Mounting Assembly-See FMA-04A 1. Input and output signal voltage referenced to supply common. 2. Output is short circuit protected to common. Ordering Information DO NOT CONNECT TO ±Vs. 3. Adjustable to zero. Filter Type Transfer Function 4. Units operate with or without offset pin connected. L - Low Pass H - High Pass B - Butterworth L - Bessel E - elliptic D80 - constant delay DC Offset Adjustment ± Vs 818L8E-5 Do not connect if trim is not required. 20 k Ω (Cermet) Model Number 1 2 3 4 5 OS - Vs Tuning Range (kHz) 1kHz to 256kHz 2kHz to 512kHz 3kHz to 768kHz 4kHz to 1,024kHz 5kHz to 1,280kHz Minimum Step (kHz) 1kHz 2kHz 3kHz 4kHz 5kHz We hope the information given here will be helpful. The information is based on data and our best knowledge, and we consider the information to be true and accurate. Please read all statements, recommendations or suggestions herein in conjunction with our conditions of sale which apply to all goods supplied by us. We assume no responsibility for the use of these statements, recommendations or suggestions, nor do we intend them as a recommendation for any use which would infringe any patent or copyright. IN-00818-01 7 25 Locust St, Haverhill, Massachusetts 01830 • Tel: 800/252-7074, 978/374-0761 • FAX: 978/521-1839 e-mail: [email protected] • Web Address: http://www.freqdev.com 8-Pole Bessel Appendix A Low-Pass Theoretical Transfer Characteristics 1 f/fc Amp Phase Delay (Hz) (dB) (deg) (sec) 0.00 0.00 0.00 .506 0.10 -0.029 -18.2 .506 0.20 -0.117 -36.4 .506 0.30 -0.264 -54.7 .506 0.40 -0.470 -72.9 .506 0.50 -0.737 -91.1 .506 0.60 -1.06 -109 .506 0.70 -1.45 -128 .506 0.80 -1.91 -146 .506 0.85 -2.16 -155 .506 0.90 -2.42 -164 .506 0.95 -2.71 -173 .506 1.00 -3.01 -182 .506 -3.67 1.10 -200 .506 -4.40 1.20 -219 .506 -5.20 1.30 -237 .506 1.40 -6.10 -255 .505 1.50 -7.08 -273 .504 1.60 -8.16 -291 .502 1.70 -9.36 -309 .498 1.80 -10.7 -327 .492 1.90 -12.1 -345 .482 2.00 -13.7 -362 .468 2.25 -18.1 -402 .417 2.50 -23.1 -436 .352 2.75 -28.3 -465 .291 3.00 -33.4 -489 .241 3.25 -38.3 -509 .201 3.50 -43.1 -526 .170 4.00 -51.8 -552 .126 5.00 -66.8 -587 .077 6.00 -79.2 -610 .052 7.00 -89.8 -626 .038 8.00 -99.0 -638 .029 9.00 -107 -647 .023 10.0 -114 -655 .018 Frequency Response Amp (dB) 0 -40 -60 -80 -100 0.1 2 3 4 5 6 78 1.0 2 3 4 5 6 7 10.0 Normalized Frequency(f/fc) Delay (Normalized) Delay (sec) 1.0 0.5 0.0 0.1 0.15 2 3 4 5 6 7 89 1.0 1.5 Normalized Time (1/f sec) Step Response (V/V) Step Response 1.Normalized Group Delay: The above delay data is normalized to a corner frequency of 1.0Hz.The actual delay is the normalized delay divided by the actual corner frequency (fc). Actual Delay = -20 1.2 1.0 0.8 0.6 0.4 0.2 -0.0 -0.2 0 1 2 3 4 Normalized Time (1/f sec) Normalized Delay Actual Corner Frequency (fc) in Hz 4 25 Locust St., Haverhill, Massachusetts 01830 ∑Tel:800/252-7074, 978/374-0761 ∑FAX:978/521-1839 e-mail: [email protected] ∑Web Address: http://www.freqdev.com ∑Fax on Demand: 978/521-5178 5 Low-Pass 8-Pole Appendix A Butterworth Theoretical Transfer Characteristics 1 f/fc Amp Phase Delay (Hz) (dB) (deg) (sec) 0.00 0.00 0.00 .816 0.10 0.00 -29.4 .819 0.20 0.00 -59.0 .828 0.30 0.00 -89.1 .843 0.40 0.00 -120 .867 0.50 0.00 -152 .903 0.60 -0.001 -185 .956 0.70 -0.014 -221 1.04 0.80 -0.121 -261 1.19 0.85 -0.311 -283 1.29 0.90 -0.738 -307 1.40 0.95 -1.58 -333 1.48 1.00 -3.01 -360 1.46 1.10 -7.48 -408 1.17 1.20 -12.9 -445 .873 1.30 -18.2 -472 .672 1.40 -494 .540 -23.4 1.50 -511 .448 -28.2 1.60 -526 .380 -32.7 1.70 -539 .328 -36.9 1.80 -550 .287 -40.8 1.90 -44.6 -560 .253 2.00 -48.2 -568 .226 2.25 -56.3 -586 .174 2.50 -63.7 -600 .139 2.75 -70.3 -611 .113 3.00 -76.3 -621 .094 3.25 -81.9 -629 .080 3.50 -87.1 -635 .069 4.00 -96.3 -646 .052 5.00 -112 -661 .033 6.00 -125 -671 .023 7.00 -135 -678 .017 8.00 -144 -683 .013 9.00 -153 -687 .010 10.0 -160 -691 .008 Frequency Response Amp (dB) 0 -40 -60 -80 -100 0.1 2 3 4 5 6 78 1.0 2 3 4 5 67 10.0 Normalized Frequency(f/fc) Delay (Normalized) Delay (sec) 2.0 1.0 0.0 0.1 0.15 2 3 4 5 6 7 8 9 1.0 1.5 Normalized Time (1/f sec) Step Response (V/V) Step Response 1.Normalized Group Delay: The above delay data is normalized to a corner frequency of 1.0Hz.The actual delay is the normalized delay divided by the actual corner frequency (fc). Actual Delay = -20 1.2 1.0 0.8 0.6 0.4 0.2 -0.0 0 1 2 3 4 Normalized Time (1/f sec) Normalized Delay Actual Corner Frequency (fc) in Hz 9 25 Locust St., Haverhill, Massachusetts 01830 ∑Tel :800/252-7074, 978/374-0761 ∑FAX:978/521-1839 e-mail: [email protected] ∑Web Address: http://www.freqdev.com ∑Fax on Demand: 978/521-5178 5 8-Pole, 6-Zero Constant Delay Appendix A Low-Pass (80 dB) Theoretical Transfer Characteristics 1 f/fc Amp Phase Delay (Hz) (dB) (deg) (sec) 0.00 0.00 .852 0.00 0.017 -30.7 .852 0.10 0.058 -61.3 .852 0.20 0.099 -92.0 .852 0.30 0.105 -123 .852 0.40 0.034 -153 .852 0.50 -0.157 -184 .852 0.60 -0.510 -215 .852 0.70 -1.07 -245 .851 0.80 -1.44 -261 .850 0.85 -1.89 -276 .849 0.90 -2.41 -291 .846 0.95 -3.01 -306 .841 1.00 -4.50 -336 .821 1.10 -6.39 -365 .783 1.20 -11.3 -417 .656 1.40 -17.1 -459 .512 1.60 -23.2 -492 .396 1.80 -29.1 -517 .312 2.00 -36.3 -542 .239 2.25 2.50 -43.4 -561 .189 2.75 -50.3 -576 .153 3.00 -57.6 -589 .127 3.25 -62.5 -599 .107 3.50 -75.4 -608 .092 3.75 -98.3 -616 .079 4.00 -86.3 -442 .069 4.25 -84.1 -448 .061 4.50 -85.1 -454 .054 4.75 -87.9 -458 .049 5.00 -92.8 -462 .044 5.25 -104 -466 .040 5.50 -101 -289 .036 5.75 -93.3 -293 .033 6.00 -89.9 -295 .030 -86.6 -300 .026 6.50 -85.1 -305 .022 7.00 -84.1 -312 .017 8.00 -84.3 -317 .013 9.00 -84.9 -321 .011 10.0 Frequency Response Amp (dB) 0 -40 -60 -80 -100 0.1 2 3 4 5 6 78 1.0 2 3 4 5 6 7 10.0 Normalized Frequency(f/fc) Delay (Normalized) Delay (sec) 1.0 0.5 0.0 0.1 0.15 2 3 4 5 6 7 89 1.0 1.5 Normalized Time (1/f sec) Step Response (V/V) Step Response 1.Normalized Group Delay: The above delay data is normalized to a corner frequency of 1.0Hz.The actual delay is the normalized delay divided by the actual corner frequency (fc). Actual Delay = -20 Normalized Delay 1.2 1.0 0.8 0.6 0.4 0.2 -0.0 -0.2 0 1 2 3 4 Normalized Time (1/f sec) Actual Corner Frequency (fc) in Hz 21 25 Locust St., Haverhill, Massachusetts 01830 ∑Tel :800/252-7074, 978/374-0761 ∑FAX:978/521-1839 e-mail: [email protected] ∑Web Address: http://www.freqdev.com ∑Fax on Demand: 978/521-5178 5 8-Pole, 6-Zero Elliptic, 1.77 Appendix A Low-Pass Theoretical Transfer Characteristics 1 f/fc Amp Phase Delay (Hz) (dB) (deg) (sec) 0.00 0.00 0.00 0.713 0.10 -0.004 -25.7 0.716 0.20 -0.014 -51.6 0.724 0.30 -0.024 -77.9 0.740 0.40 -0.020 -105 0.767 0.50 0.007 -133 0.811 0.55 0.022 -148 0.840 0.60 0.033 -163 0.872 0.65 0.031 -179 0.908 0.70 0.014 -196 0.946 0.75 -0.015 -213 0.989 0.80 -0.041 -232 1.04 0.85 -0.046 -251 1.12 0.90 -0.016 -272 1.23 0.95 -0.025 -296 1.40 1.00 -0.035 -323 1.65 1.10 -1.76 -392 2.14 1.20 -8.28 -467 1.86 1.30 -18.4 -522 1.19 1.40 -29.3 -558 0.753 1.50 -40.1 -578 0.517 1.60 -51.5 -594 0.381 1.70 -65.2 -606 0.296 1.75 -75.0 -611 0.265 1.80 -113.0 -616 0.239 1.85 -83.6 -440 0.217 1.90 -82.0 -444 0.198 1.95 -83.7 -447 0.182 2.00 -87.8 -450 0.168 2.20 -85.8 -280 0.126 2.40 -82.0 -289 0.099 2.60 -83.5 -295 0.081 2.80 -88.2 -301 0.067 3.00 -99.9 -305 0.057 3.50 -87.2 -134 0.040 4.00 -83.1 -140 0.030 5.00 -82.1 -148 0.018 6.00 -83.1 -154 0.013 7.00 -84.6 -157 0.009 8.00 -86.2 -160 0.007 9.00 -87.8 -163 0.005 10.0 -89.3 -164 0.004 Frequency Response Amp (dB) 0 -40 -60 -80 -100 0.1 2 3 4 5 6 78 1.0 2 3 4 5 6 7 10.0 Normalized Frequency(f/fc) Delay (Normalized) Delay (sec) 4.0 2.0 0.8 0.0 0.1 0.15 2 3 4 5 6 7 89 1.0 1.5 Normalized Time (1/f sec) Step Response (V/V) Step Response 1.Normalized Group Delay: The above delay data is normalized to a corner frequency of 1.0Hz.The actual delay is the normalized delay divided by the actual corner frequency (fc). Actual Delay = -20 1.2 1.0 0.8 0.6 0.4 0.2 -0.0 0 1 2 3 4 Normalized Time (1/f sec) Normalized Delay Actual Corner Frequency (fc) in Hz 24 25 Locust St., Haverhill, Massachusetts 01830 ∑Tel :800/252-7074, 978/374-0761 ∑FAX:978/521-1839 e-mail: [email protected] ∑Web Address: http://www.freqdev.com ∑Fax on Demand: 978/521-5178 5 High-Pass 8-Pole Appendix A Butterworth Theoretical Transfer Characteristics 1 f/fc Amp Phase Delay (Hz) (dB) (deg) (sec) 0.10 -160 691 0.819 0.20 -112 661 0.828 0.30 -83.7 631 0.843 0.40 -63.7 600 0.867 0.50 -48.2 568 0.903 0.60 -35.5 535 .956 499 0.70 -24.8 1.04 459 0.80 -15.6 1.19 437 0.85 -11.6 1.29 413 0.90 -8.06 1.40 0.95 -5.15 386 1.48 360 1.00 -3.01 1.46 275 1.20 -0.229 0.873 226 1.40 -0.020 0.540 -0.002 194 1.60 0.380 170 1.80 0.00 0.287 152 0.00 2.00 0.226 120 0.139 0.00 2.50 0.094 0.00 99.2 3.00 0.052 0.00 74.0 4.00 5.00 0.00 59.0 0.033 49.0 0.023 6.00 0.00 0.00 42.1 0.017 7.00 0.00 36.8 0.013 8.00 0.00 32.7 0.010 9.00 10.0 0.00 29.4 0.008 Frequency Response Amp (dB) 0 -20 -40 -60 -80 -100 0.1 2 3 4 5 6 78 1.0 2 3 4 5 6 7 10.0 Normalized Frequency(f/fc) 1.Normalized Group Delay: The above delay data is normalized to a corner frequency of 1.0Hz.The actual delay is the normalized delay divided by the actual corner frequency (fc). Actual Delay = Normalized Delay Actual Corner Frequency (fc) in Hz 29 25 Locust St., Haverhill, Massachusetts 01830 ∑Tel :800/252-7074, 978/374-0761 ∑FAX:978/521-1839 e-mail: [email protected] ∑Web Address: http://www.freqdev.com ∑Fax on Demand: 978/521-5178 8-Pole, 6-Zero Elliptic, 1.77 Appendix A High-Pass Theoretical Transfer Characteristics 1 f/fc Amp Phase Delay (Hz) (dB) (deg) (sec) 0.10 -89.3 164 0.440 0.20 -82.1 148 0.459 0.30 -90.6 131 0.495 292 0.40 -82.4 0.559 -87.8 450 0.50 0.671 0.55 -90.0 0.761 437 -60.2 0.60 0.890 603 -32.4 0.70 1.37 563 -13.1 0.80 2.35 498 -6.28 0.85 2.77 451 0.90 -2.21 401 2.66 358 0.95 -0.51 2.15 324 1.00 -0.03 1.64 277 1.10 -0.01 1.04 225 1.20 -0.05 0.757 1.30 -0.03 221 0.596 1.40 0.01 201 0.486 1.50 0.03 185 0.409 1.60 0.03 172 0.347 1.70 0.03 160 0.299 1.80 0.02 150 0.260 1.90 0.01 141 0.229 2.00 0.01 133 0.203 2.50 -0.02 105 0.123 3.00 -0.02 86.9 0.083 4.00 -0.02 64.7 0.046 5.00 -0.01 51.6 0.029 6.00 -0.01 42.9 0.020 -0.01 0.015 7.00 36.8 -0.01 0.011 8.00 32.1 9.00 -0.01 28.6 0.009 10.0 0.00 25.7 0.007 Frequency Response Amp (dB) 0 -20 -40 -60 -80 -100 0.1 2 3 4 5 6 78 1.0 2 3 4 5 67 10.0 Normalized Frequency(f/fc) 1.Normalized Group Delay: The above delay data is normalized to a corner frequency of 1.0Hz.The actual delay is the normalized delay divided by the actual corner frequency (fc). Actual Delay = Normalized Delay Actual Corner Frequency (fc) in Hz 37 25 Locust St., Haverhill, Massachusetts 01830 ∑Tel :800/252-7074, 978/374-0761 ∑FAX:978/521-1839 e-mail: [email protected] ∑Web Address: http://www.freqdev.com ∑Fax on Demand: 978/521-5178