Band-pass filter design

Transcription

1 1 Band-pass filter design To separate signals with low frequencies (< 10kHz) from their spectrum, a filter was needed. A filter build with a single coil (solenoid) and capacitor was mostly unsufficient to pass a digital signal without distortion. With the transmission of Morse signals, where the carrier-frequency will be switched between ON and OFF by the MORSE-key (A1 modulation) and the later on digitizing of other information, it was necessary to receive and operate these signals as clear as possible without distortion. By the operation of digital signals the contour and the frequency-contents (the loss of higher harmonic frequencies) will be disturbed by the use of a too narrow band-pass filter. Therefore the frequency-passing for modulated frequencies must be as wide as possible. To suppress the nearby frequencies a more sophisticated filter was needed. This band-pass filter was build up in its simplest way with two coupled singular tuned circuits. The coupling for this application of inductive and capacitive parts of the filter, was performed by a capacitor. The inductive parts must have the ability to be tuned. 1 Application of a band-pass filter for the use with Morse-signals transmitted by keying The supposition was made that the hand-transmitted information could not be generated quicker than with the velocity of 75 BAUD, conform 75 bits (marks) per second, is also a frequency of 75 Hz. For the assumption that the carrier for the Morse-signal (p.e Hz) could be shifted a little and that the distortion for the digital signal must be as low as possible, the bandwidth of that filter was designed for a 200 Hz width. The bandwidth is the width where the amplitude of the lowest and highest frequencies to be passed, ceased about -3 db (0.7 of the Vmax) according the central carrier-frequency. 2 The parts of the constructed band-pass filter To limit the dimensions of the components of the filter, a selection was made for the solenoids (selfinductances) to be tuned in Ferroxcube (Siferrite) pot cores. The high magnetic permeability of those pot cores was important for this application. The magnetic permeability is a number for an item for its behavior within a magnetic field. The permeability is according the level an item can be magnetized. The absolute permeability µ of a magnetised body is: The induction that will be derived by the strength of a magnetic field within it consists:

2 2 µ = B/H B: Total flux for an area partition (field density) = Induction H: magnetic field in Ampère/m 2 The former existing pot-cores with the dimensions of 18 mm Ø and 11 mm height with the code: 2000N28 of the company Siemens, were appropriate for self-inductances at lower frequencies. The µ value, transferred to the square-value for the self-inductance per winding was at 1500 Hz frequency, about 400 nh/w 2. This value was true within a hermetic closed potcore without an air-gap. To tune the band-pass filter precisely at the required central frequency and bandwidth potcores were chosen with an air-gap, which value µ for the self-inductance could be changed by the use of a tuning helix. The quality-factor Q for each solenoid and the coupling-factor k define together the bandwidth and flatness of the filter-characteristic. For the value kq=1,2 a nearly flat passingcharacteristic will be derived. For larger values of kq, a dip in the middle of the passing-band arise. Both LC circuits had to be tuned to the same frequency. To derive the coupling between both LC circuits the BUTTERWORTH mathematics was used. 3 Butterworth small band-pass filter First of all the attenuation for the frequencies outside the filter were determined. Because the nearby operating-frequencies were positioned about 2000Hz away, a filter with an upmost passing bandwidth of ±1000 Hz was sufficient. With an effective band-width of 150 to 200 Hz, the scale of attenuation is 2000/200 = 10. The filter-lists determine for a double tuned narrow-band filter with n=2 elements with an attenuation-factor of 10 and a suppression of at least -40 db in power, corresponding an attenuation for voltages at a ratio of -100.

3 3 Calculated is AdB = 10 log [ 1 + ( 2000/200) 4 ] = 10 log = 10 x 4, = 40,00043dB in power (= 100,005 voltage attenuation) 4 Design of the Butterworth narrow-band filter The central frequency is 1.5 khz, the bandwidth is 200 Hz, the attenuation for the band-pass is than 2000/20 = 10 (QBw) multiplied by (Q n) for a double filter is: 10 X = in total. Butterworth narrow-band filter In the figure a Butterworth narrow-band filter is shown with two circuits (L 1/C 2 and L 2/C 4), coupled by the capacitor C 3. The value for that capacitor was selected for a critical coupling of the filter-parts. C 1 and C 5 are coupling capacitors to match the filter-impedances at the elements of the electrical circuits at which the narrow-band filter would be part of. The values for the solenoids L 1 and L 2 and those of the capacitors C 2 and C 4 could then be defined. Remark: The input-impedance Z in and the output-impedance Z out could also be matched by a tap at the input- and output- solenoid (coil). The input- and output-impedance of the filter-unit was then transformed with the square of the ratio of the tap windings to the total number of coil-windings. 5 Calculations for a Butterworth narrow-band filter Basic formulas: 1. Filter impedance (Z0) = Qn x QBw x 2 x pi x Fo x L 2. LC = / (Fo x Fo); with Fo in MHz LC ~ 12.x Co = LC / L 4. C3 = Co x [1,414 / (Qn x QBw)]

4 4 5. C2 = Co - C1 - C3 6. C4 = Co - C3 - C5 For formula 2 above, we found for a center-frequency of MHz, LC = 11 * If LC is about 11 * 10 9 and a value for C 0 of pf, then the self-inductance of L is about 400 mh (Z l = Z c = ~4000Ω ) C 3 = pf x [ 1.414/ (Q n x QBw)] = ~ 2700 pf. Remark: The capacitors C 1 and C 5 were not applied for this filter. For the filter of the image, a critical coupled test-filer with a central frequency of 1500 Hz was used. The coupling-capacitor C 3 had a value of 820 pf. With that value of the coupling capacitor, the deformation for a Morse signal with the rate of 75 Baud was determined. The next figure shows the elements for the filtering and further operation of a 1500 Hz modulated ON- OFF signal to a digital signal. The overcritical coupled 1500 Hz filter L 1-C 1 and L 2-C 3 (coupling capacitor C 2 = 3900 pf) is followed by a transformer L 3 (build up with a Ferroxcube pot-core, without an air-gap). This transformer was matched with a tap at the output-impedance of the band-pass filter. With a double rectifier as demodulator the original ON-OFF Morse-signal (max 200 BAUD) was coupled to the input of an operational amplifier IC1 with back-coupling. The output of this amplifier was the input for the peakdetector IC2 that generated a complete digital signal, switching between -12V and +12 V.

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