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ENCYCLOPEDIA OF RADIO ELECTRONICS AND ELECTRICAL ENGINEERING Calculation of strip microwave filters. Encyclopedia of radio electronics and electrical engineering
Encyclopedia of radio electronics and electrical engineering / Radio amateur designer The author introduces readers to the computer program "BPF-PP" developed by him for calculating the parameters of narrow-band microwave filters. The "BPF-PP" program described below makes it possible to calculate narrow-band filters on coupled half-wave resonators. I hope that it will be of interest to radio amateurs developing microwave devices. The program is written in the GWBASIC programming language, can be easily transformed into BASIC of any version and is designed for a user who has prior knowledge of microstrip line (MPL) technology and electrical filters. The reader will find additional information in the technical literature, a list of which is presented at the end of the article. In order to quickly gain skills in using the program, let's consider a specific calculation example. In the text, the contents of the program displayed on the screen are indicated in quotation marks. Let us assume that preliminary calculations or design considerations have shown the need to create a second-order filter with a bandwidth of 694 to 734 MHz. Let's make it on the basis of double-sided foil fiberglass. After starting the program, the following message will appear on the monitor screen: "The filter type is indicated: Butterworth (2-9 orders) - V; Chebyshev (3-9 orders) - T. Filter order (2-9)?". For this question, in our example, we will enter the number 2 from the keyboard. Further: "filter type - B load resistance, Ohm? fifty Bandwidth limits, GHz: Upper? .734 lower? .694 Passband center frequency F0 = 0.7137186 GHz" On request "Foil thickness t, mm? Substrate thickness H, mm? the dimensions in millimeters of the material used must be entered. Let's say the thickness of the foil is t = 0,05 mm, and the fiberglass substrate is H = 1,5 mm. And to the query "Dielectric constant E?" we introduce for our example E = 4,8. Following this, the results of the calculation will appear on the screen: " *********** CALCULATION IN PROGRESS ********** width of bonded strips W(0) =2.67 mm clearance S(0,1) = 0.14 mm quarter wave - 52.15 mm width of connected strips W(1) = 3.17 mm clearance S(1,2) = 3.13 mm quarter wave - 51.65 mm bonded strip width W(2) = 2.67 mm clearance S(2,3) = 0.14 mm quarter wave - 52.15 mm" Based on the results of the calculation, we make the following decision: on one side of the plate of foil fiberglass, we place two strips of foil with a width W (0) and a length of 5,215 cm with a gap S (0,1) between them. We place the second pair of connected strips on the same side of the plate on the right, close to the first, and the upper strip of the second pair should be a continuation of the lower strip of the first pair (see figure), but with its own width W(1). The second strip of the second pair, 5,165 cm long, is placed with a gap S(1,2) under the first.
The first strip 5,215 cm long of the third pair with width W(2) continues the second of the second pair. The second strip of the third pair, 5,215 cm long and W(2) wide, will be under the first with a gap S(2,3). The foil on the second side of the plate is left solid and intact. Thus, we obtain a structure of four strip lines located one below the other with gaps S(0,1), S(1,2), S(2,3) and shifted in length by a quarter of a wave. The two inner strips serve as half-wave resonators, and the two outer ones serve as quarter-wave coupling elements with the generator and the load. To the extreme ends of the outer strips, a matched load and a generator or lines are connected, having a wave impedance the same as that of the filter. A few words about the program. Command lines from 80th to 240th are a table with filter parameters - Butterworth prototypes from the second to the ninth orders and Chebyshev from the third to the ninth orders with a passband ripple of 0,28 dB, which is sufficient for amateur practice in most cases.
If necessary, instead of the table of prototypes, a subroutine can be introduced that determines the coefficients of the prototype filters of higher orders and with other non-uniformity values. It should be noted that for better convergence of practical results with the calculated ones, it is necessary to first measure the dielectric permittivity of the glass fiber laminate of the plate used. To do this, it is necessary to make a strip line of arbitrary length on another plate of the same material, which will serve as a half-wave resonator. Near one of its ends, the same line is placed in parallel with a gap (close to real), but 5 ... 10 times shorter in length. This line will act as a resonator exciter. To do this, a generator is connected to one of its ends, and the other is loaded with a 50 Ohm resistor, selected in advance. At the resonance frequency, exactly in the middle of the resonator, a voltage node is formed, which is fixed by the detector head. The effective permittivity is determined from the expression
where h is the thickness of the fiberglass, mm; W is the width of the resonator strip, mm. To make measurements of the permittivity more reliable, one should choose a rather large resonator length - 150...200 mm. In this case, the presence of an end capacitance will introduce only a minor error. When making such measurements, I usually choose the width of the gap between the exciting line and the resonator, as well as the width of the line and the resonator, to be equal to twice the thickness of the substrate. Measurements are carried out at a frequency of no more than 1 GHz. Literature
Author: O.Soldatov, Tashkent, Uzbekistan
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, where Fres - resonance frequency in MHz; L is the length of the resonator in meters. The value of the dielectric constant e of the material (enter the program with the letter E) is obtained from the formula
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