Mini-Circuits Band Pass Filters with Linear Phase Response ® Filters with linear phase response are desirable, due to their ﬂat group delay, in many applications, for example in image processing and digital data transmission. Such ﬁlters maximally preserve the wave shape of the pasing signal, since they delay all frequency components of the signal by the same amount (i.e. do not cause phase distortion). Deﬁnitions Phase response φ(ω) (also “Phase Shift” or “Insertion Phase”) of a ﬁlter is deﬁned as the phase (or complex angle) of the frequency response. Group delay Tg is the amount of time it takes for a signal having ﬁnite time duration, such as a pulse, to pass through the ﬁlter. Group delay is deﬁned as the derivative of the phase shift through the ﬁlter with respect to frequency: Tg = – dφ 1 = – dω 2p dφ df Linear phase is a property of a ﬁlter, where the phase response is a linear function of frequency and, consequently the group delay is constant at all frequencies (ﬂat time delay). This enables the transmission of various frequency components contained in a modulated waveform to be delayed by the same amount while traveling through the ﬁlter thus preserving the modulation wave shape and avoiding phase distortion. Linear phase response can be presented at ﬁlter speciﬁcation either by mean of “Group Delay Variation” or by mean of “Deviation From Linear Phase”. The “Deviation From Linear Phase” is deﬁned as a distance of each point of a real ﬁlter Insertion Phase from the ideal ﬁlter Insertion Phase (straight line), as presented at Figure 1 below. Figure 1: Phase Deviation From Linear Phase of a Real Filter Phase (deg) Ideal filter Real filter Frequency Phase deviation from linear phase The coefﬁcients of the ideal ﬁlter (straight line y=ax+b) are calculated according to following formulas (“Least square” method): n a= i=1 n n i=1 2 n i=1 2 n∑xi – (∑xi) i=1 Where n n∑xiyi – ∑xi ∑yi n , b= n ∑ y i – a∑ x i i=1 i=1 n i=1 x is Frequency point, y is Insertion Phase (normalized to 360o) and n is the number of frequency points. Retrieving Deviation From Linear Phase of a Filter Deviation From Linear Phase is received by subtracting the calculated Ideal Insertion Phase from the measured Insertion Phase (S21). Mini-Circuits ® EW ALL N minicircuits.com ISO 9001 ISO 14001 CERTIFIED P.O. Box 350166, Brooklyn, New York 11235-0003 (718) 934-4500 Fax (718) 332-4661 For detailed performance specs & shopping online see Mini-Circuits web site The Design Engineers Search Engine Provides ACTUAL Data Instantly From MINI-CIRCUITS At: www.minicircuits.com RF/IF MICROWAVE COMPONENTS This document and its contents are the property of Mini-Circuits. REV. OR M113292 AN-75-004 070830 Page 1 of 3 Mini-Circuits ® Test results of Mini-Circuits BPF model RBP-263 Mini-Circuits offers several Band Pass Filters with linear phase response (currently available RBP-220+, RBP-263+ and RBP-275+). Figures 2 - 4 show the typical data, graphs and outline drawing RBP-263+, for which the deviation from linear phase is deﬁned as ±8º typ. at Center Frequency ± 43MHz. Visit Mini Circuits website for detailed speciﬁcations. Figure 2: Typical Performance Data of RBP-263+ Frequency (MHz) Insertion Loss (dB) VSWR (:1) Frequency (MHz) Deviation from Linear Phase (deg) 1.0 10.0 80.0 120.0 140.0 200.0 99.02 75.88 41.13 31.89 27.77 9.98 579.06 289.53 96.51 59.91 43.44 3.48 220.5 224.0 230.0 235.0 240.0 246.0 6.30 2.83 0.21 -2.20 -2.87 -2.87 220.5 230.0 263.5 297.0 306.5 2.35 1.47 1.12 1.63 2.66 2.04 1.40 1.17 1.12 1.81 251.0 255.0 263.5 266.0 271.0 -2.26 -1.43 0.27 0.96 1.82 325.0 350.0 360.0 400.0 500.0 1000.0 9.58 23.83 30.23 40.61 41.00 56.91 7.94 27.59 34.75 54.29 72.39 82.73 275.0 284.0 291.0 297.0 302.0 306.5 2.49 3.06 2.26 -0.32 -3.47 -8.02 Figure 3: Measured Insertion Phase and Phase Deviation of RBP-263+ Band Pass Filter RBP-263+ Insertion Phase and Phase Deviation from Linear Phase 15 A Insertion Phase (deg) 50 10 B 0 5 -50 0 C -100 -150 -200 220 -5 -10 230 240 250 260 270 280 290 300 Phase Deviation from Linear (deg) 100 -15 310 Frequency (MHz) Measured Insertion Phase Calculated Linear Phase Phase Deviation from Linear Points A, B, C indicate places where the phase of a real ﬁlter equals to the phase of ideal ﬁlter (i.e. phase deviation is 0). Mini-Circuits ® EW ALL N minicircuits.com ISO 9001 ISO 14001 CERTIFIED P.O. Box 350166, Brooklyn, New York 11235-0003 (718) 934-4500 Fax (718) 332-4661 For detailed performance specs & shopping online see Mini-Circuits web site The Design Engineers Search Engine Provides ACTUAL Data Instantly From MINI-CIRCUITS At: www.minicircuits.com RF/IF MICROWAVE COMPONENTS Page 2 of 3 Mini-Circuits ® Figure 4: Outline drawing of Mini-Circuits RBP family of ﬁlters Outline Drawing TOP SIDE SIDE VIEW PCB Land Pattern BOTTOM SIDE METALLIZATION SOLDER RESIST Outline Dimensions ( inch mm ) A B C D E F G H J K L M N P Q R wt. .350 .350 .100 .175 .075 .100 .090 .040 .080 .050 .040 .195 .390 .120 .390 .070 grams 8.89 8.89 2.54 4.45 1.93 2.54 2.29 1.02 2.03 1.27 1.02 4.95 9.91 3.05 9.91 1.78 0.25 Mini-Circuits ® EW ALL N minicircuits.com ISO 9001 ISO 14001 CERTIFIED P.O. Box 350166, Brooklyn, New York 11235-0003 (718) 934-4500 Fax (718) 332-4661 For detailed performance specs & shopping online see Mini-Circuits web site The Design Engineers Search Engine Provides ACTUAL Data Instantly From MINI-CIRCUITS At: www.minicircuits.com RF/IF MICROWAVE COMPONENTS Page 3 of 3

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