FCC2 LOW Pass 7th Order Elliptical Filter · The low pass filter is a 7th order elliptic designed ... order elliptical filter with 3db cutoff at 31 Mhz, -60db stop ... Low_Pass_7th_Order_Elliptical_Filter-Small

FCC2 LOW_Pass_7th_Order_Elliptical_Filter

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 2009 All rights Reserved

FCC2 LOW_Pass_7th_Order_Elliptical_Filter 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



Calculated The documentation states that a 7th 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 12.19. The design of a 7th order elliptical filter with 3db cutoff at 31 Mhz, -60db stop band and 0.2 ripple in the pass band. Get coefficients from table 12.19 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) 7 1.257 1.244 0.1348 1.716 0.9025 0.6672 1.527 0.9477 0.4718 1.001

For the capacitors

o C = G(x) or H(x)/ cR * Calculate c

c = 2 Fc c = 2 * 3.1416 * 31Mhz c = 1.95e08

Calculate cR * cR * = R * 1.95e08 cR * = 7.79e10

C1 = 1.257 / 7.79e10 C1 = 16.13 pf

C2 = 0.1348 / 7.79e10 C2 = 1.73 pf

C3 = 1.716 */7.79e10 C3 = 22.02 pf

C4= 0.6672 / 7.79e10 C4 = 8.56 pf

C5= 1.527 / 7.79e10 C5 = 19.6 pf

C6= 0.4718 / 7.79e10 C6 = 6.06 pf

C7= 1.001 / 7.79e10 C7 = 12.87 pf

For the inductors

o C = G(x) * c

R

Calculate c

R



c

R

= 400 / 1.95e08

c

R

= 2.05e-6

L1 = 1.244 * 2.05e-6 L1 = 2.55 uH

L2 = 0.9025 * 2.05e-6 L2 = 1.85 uH

L3 = 0.9477 * 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 (1st frequency that meets the stop band attenuation) was chosen when the coefficients were chosen. o Fstop = Fc * 1.269

Fstop = 31 Mhz * 1.269 Fstop = 39.34 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



Simulation

I simulated both the circuit used in the FCC2 and my nearest approximation. Frequency

FCC2 Design o Fc = 34.86 Mhz

My Closest Approximation

o Fc = 31.3 Mhz

Ripple FCC2 Design

o Ripple = 1.92 – -0.05 o Ripple = 1.97 db

My Closest Approximation o Ripple = 2.37 – -0.05 o Ripple = 2.42 db

VDB(in)VDB(out)VDB(out1)

Low_Pass_7th_Order_Elliptical_Filter-Small Signal AC-13-Graph

Frequency30.000M20.000M10.000M

3.5003.0002.5002.0001.5001.000

500.000m0.0

-500.000m-1.000-1.500-2.000-2.500-3.000-3.500-4.000-4.500-5.000-5.500-6.000-6.500-7.000-7.500-8.000-8.500

Stop Band Attenuation FCC2 Design

o Stop Band Attenuation = -56.7 db My Closest Approximation

o Stop Band Attenuation = -46.3 db




Low_Pass_7th_Order_Elliptical_Filter-Small Signal AC-14-Graph

Frequency100.000M 1.000G 10.000

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Fstop Frequency

FCC2 Design o Fstop = -48.51 Mhz

My Closest Approximation o Fstop = -39.22 Mhz


william-Small Signal AC-16-Graph

Frequency100.0090.000M80.000M70.000M60.000M50.000M40.000M30.000M

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Insertion Loss FCC2 Design

o Insertion Loss = 0 dB My Closest Approximation

o Insertion Loss = 0 dB


FCC2 LOW_Pass_7th_Order_Elliptical_Filter 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 = 2.22 – -3.85

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



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

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Freq Mhz

Gai

n d

b

Measured


FCC2 LOW_Pass_7th_Order_Elliptical_Filter 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



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



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



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

SimulationApprox.

SimulationFCC2

Design

Calculated Documentation

Fc MHz 25.5 31.3 34.86 31 31Ripple db 6.07 2.02 1.97 0.2 N/AStop Bandwidth Attenuation db

N/A -46.3 -56.7 -60 N/A

Fstop Mhz N/A -39.22 -48.51 39.34 Insertion Loss db

0 0 0 0 N/A

The graph below shows a comparison of the frequency responses.

o The measured frequency response shows the same general trends

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Measured

Sim FCC2 Design

Sim Approximation




References

1. Okas, Robert, W3CD, The Norcal FCC-2 Mark II Assembly & Operating Manual Rev. 1 6-7-08 (NORCAL 2008), http://www.norcalqrp.org/files/NorCal%20FCC2_MKII_assy_V1.pdf, online, accessed 2009.

2. UNKNOWN, 2009 ARRL Handbook For Radio Communications, (ARRL 2009), Tables 12.19 p12.16.

http://www.norcalqrp.org/files/NorCal%20FCC2_MKII_assy_V1.pdf

Documents

FCC2 LOW Pass 7th Order Elliptical Filter · The low pass filter is a 7th order elliptic designed ... order elliptical filter with 3db cutoff at 31 Mhz, -60db stop ... Low_Pass_7th_Order_Elliptical_Filter-Small