FCC2 LOW_Pass_7th_Order_Elliptical_Filter
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1 V1 is sinusoidal Top circuit_1 is filter as appears in FCC2 Schematic Bottom circuit_2 is filter built with ARRL 2009 tables (ripple = 0.2 Stop Band Depth = - 60 Fstop = 1.269) William R. Robinson Jr. p1of 13
2 Purpose and Function The filter attenuation increases rapidly above 31 MHz to remove the DDS alias products. 1 Theory and Design The low pass filter is a 7th order elliptic designed for 400 Ohm input and output impedance and steep attenuation beyond 31 MHz. A deep null was placed at 75 MHz to effectively remove any clock signal from the output. 1 William R. Robinson Jr. p2of 13
3 Calculated The documentation states that a 7 th order elliptical filter is what is used for the design with a deep band stop (-70 db). The only place I could readily obtain elliptical a.k.a. Cauer filter coefficient table was the 2009 ARRL Handbook For Radio Communications 2. These tables do not have as deep of a stop band attenuation. Below I present the steps taken to Calculate the filter with a response that is closest to the stated design i.e. Table The design of a 7 th order elliptical filter with 3db cutoff at 31 Mhz, -60db stop band and 0.2 ripple in the pass band. Get coefficients from table Design has more ripple and significantly deeper stop band Order G(1) G(2) H(2) G(3) G(4) H(4) G(5) G(6) H(6) G(7) For the capacitors o C = G(x) or H(x)/ R * c Calculate c c = 2 Fc c = 2 * * 31Mhz c = 1.95e08 Calculate R * c R * c = R * 1.95e08 R * c = 7.79e10 C1 = / 7.79e10 C1 = pf C2 = / 7.79e10 C2 = 1.73 pf C3 = */7.79e10 C3 = pf C4= / 7.79e10 C4 = 8.56 pf C5= / 7.79e10 C5 = 19.6 pf C6= / 7.79e10 C6 = 6.06 pf C7= / 7.79e10 C7 = pf For the inductors R o C = G(x) * c R Calculate c William R. Robinson Jr. p3of 13
4 R = 400 / 1.95e08 c R c = 2.05e-6 L1 = * 2.05e-6 L1 = 2.55 uh L2 = * 2.05e-6 L2 = 1.85 uh L3 = * 2.05e-6 L3 = 1.95 uh Frequency The Cutoff frequency was chosen at 31 Mhz when the filter components were calculated. o Fc = 31 Mhz Ripple The ripple was chosen at 0.2 when the coefficients were chosen. o Ripple = 0.2 db Stop Band Attenuation The Stop band Attenuation was chosen at 60 db when the coefficients were chosen. o Stop Band Attenuation = -60 db Fstop Frequency The Fstop frequency (1 st frequency that meets the stop band attenuation) was chosen when the coefficients were chosen. o Fstop = Fc * Fstop = 31 Mhz * Fstop = Mhz Insertion Loss If inductors and capacitors were perfect and contained no internal resistive losses, then insertion loss for LC filters would not exist. 3 o Insertion Loss = 0 db William R. Robinson Jr. p4of 13
5 Simulation I simulated both the circuit used in the FCC2 and my nearest approximation. Frequency FCC2 Design o Fc = Mhz My Closest Approximation o Fc = 31.3 Mhz Ripple FCC2 Design o Ripple = o Ripple = 1.97 db My Closest Approximation o Ripple = o Ripple = 2.42 db VDB(in) VDB(out) VDB(out1) Low_Pass_7th_Order_Elliptical_Filter-Small Signal AC-13-Graph m m Frequency M M M Stop Band Attenuation FCC2 Design o Stop Band Attenuation = db My Closest Approximation o Stop Band Attenuation = db William R. Robinson Jr. p5of 13
6 VDB(in) VDB(out) VDB(out1) Low_Pass_7th_Order_Elliptical_Filter-Small Signal AC-14-Graph M 1.000G Frequency Fstop Frequency FCC2 Design o Fstop = Mhz My Closest Approximation o Fstop = Mhz VDB(in) VDB(out) VDB(out1) william-small Signal AC-16-Graph M M M M Frequency M M M Insertion Loss FCC2 Design o Insertion Loss = 0 db My Closest Approximation o Insertion Loss = 0 db William R. Robinson Jr. p6of 13
7 Real Circuit The filter measures very poorly compared to the simulations, showing large ripple that passes through the three db region twice. Frequency Fc = 25.5 Mhz o But another 3db at 15.9 Mhz Ripple Ripple = o Ripple = 6.07 db Stop Band Attenuation Unable to measure as I was using the FCC2 DDS and the source and it dos not go past 30 Mhz Fstop Frequency Unable to measure as I was using the FCC2 DDS and the source and it dos not go past 30 Mhz Insertion Loss Insertion Loss = 0 db William R. Robinson Jr. p7of 13
8 The graph below shows the measured frequency response. This was obtained in circuit using the DDS as the source as the only RF generator I had available to me stopped at 20 Mhz. 7th Order Elliptical FIlter Gain db Measured Freq Mhz William R. Robinson Jr. p8of 13
9 The frequency spurs get worst as the desired frequency increases. The traces below show the effects in the time and frequency domains of the filter. Time Domain measured at 10 Mhz o Top (blue) trace is input at R20 o Bottom (pink) trace is output measured at R21 Note little filtering is evident Frequency Domain measured at 10 Mhz o Top (blue) trace is input at R20 o Bottom (pink) trace is output measured at R21 Note -18db of filtering at ~35 Mhz and others is evident William R. Robinson Jr. p9of 13
10 Time Domain measured at 31 Mhz o Top (blue) trace is input at R20 o Bottom (pink) trace is output measured at R21 Note filtering is very evident William R. Robinson Jr. p10of 13
11 Frequency Domain measured at 31 Mhz o Top (blue) trace is input at R20 o Bottom (pink) trace is output measured at R21 Note -25 db of filtering at ~81 Mhz and others is very evident William R. Robinson Jr. p11of 13
12 Comparison The real circuit did not measure to far from the simulation and calculations o One cause may be that the design tables used do not go to as deep of ripple Real- Measured Simulation Approx. Simulation FCC2 Design Calculated Documentation Fc MHz Ripple db N/A Stop N/A N/A Bandwidth Attenuation db Fstop Mhz N/A Insertion Loss db N/A The graph below shows a comparison of the frequency responses. o The measured frequency response shows the same general trends Measured Sim FCC2 Design Sim Approximation William R. Robinson Jr. p12of 13
13 References 1. Okas, Robert, W3CD, The Norcal FCC-2 Mark II Assembly & Operating Manual Rev (NORCAL 2008), online, accessed UNKNOWN, 2009 ARRL Handbook For Radio Communications, (ARRL 2009), Tables p William R. Robinson Jr. p13of 13
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