CaLC3.txt 1997-03-23/ Jouni Verronen This file contains some practical examples how to use CaLC3 ----------------------------------------------------------- First the basic operating instructions copied from the info section of the program (under F1) with some addidional remarks. General: This program is a set of five calculation programs, which all are under eyes at the same time. The package is useful when calculating LC matching circuits, LC filters and complex impedances in general. A specific calculation is chosen by number. Esc or Spacebar takes back to main menu level. Left/Right arrow keys or Tab can also be used to change a calculation. An active program is indicated by a dashed line under the header. In each calculation program an input change is asked by stroking one character, the new number is given, and the results are updated immediately. All the input values and results are visible all the time. Use F9 to change units. 1. fLCX is a fast and accurate substitute for the graphic reactance chart. Stroke respective letters to give known values. New results are then calculated taking the two last given values as those known. The last input is always marked with '*' for remind. You can use a calculated value as a new known value by stroking bare enter for an input (the program does not accept 0 as an input, but takes the old value instead). The numbers you see on the screen are right at any time, in other words L and C values correspond to X and f. To use fLCX without any confusion you must know two things, which are peculiar to this program: 1) The two last given inputs are always the variables in the calculation, the rest two entities are calculated from these. If you give f and then X for example, L and C values which have reactance X at f are calculated. If you proceed by giving C, now new f and L values are calculated taking the X value given before C as the other variable. 2) If you now want to check the reactance of the just calculated L value at another frequency, you can give bare enter for L instead of bothering to type the value. Then you give frequency and the result is seen instantly. 2. Impedance Impedance section calculates transforms between the following forms: - series - parallel - polar - reflection coefficient with Zo given Additionally the following information is calculated: - circuit Q - return loss if the impedance terminates a line with Zo - mismatch loss in the case power is transmitted from a line with Zo to that complex impedance If Zo is changed, the program keeps absolute impedance constant and calculates the new complex reflection coefficient for the new characteristic impedance. Use respective numbers to give the known form. 3. X1 // X2 is for calculating the total reactance of two parallel coupled reactances, which is frequently needed in analyzing circuits. Stroke 1 and 2 to give inputs. For capacitive reactance give negative value, for inductive positive. 4. Cs + Ls is for calculating effective C or L values for a series LC circuit. Stroke f, c, l to give inputs. The two most frequent uses for Cs + Ls is to check the effective capacitance of a capacitor at a certain frequency and to find a capacitor, which is resonant at the frequency of interest to make an effective RF short. An example is given later, how to use this calculation to replace a shunt capacitor with a series LC in a low-pass filter to improve attenuation. 5. Cp // Lp is for calculating effective C or L values for a parallel LC circuit. Stroke f, c, l to give inputs. Both Cs + Ls and Cp // Lp calculate the resonant frequency fr for the LC and the effective capacitance or inductance at the given frequency f. The positive number is real. The negative number shows the element value to add, if you want to resonate LC at the given frequency f. Units You can change units at any time by stroking F9. The numbers you see on the screen after that are right with respect to each other. However, the program does not keep absolute values, just the numbers remain the same. If you e.g. have 1.8 MHz and change units to kHz, you dont automatically now have 1800 kHz on the screen, but 1.8 and have to change the numbers manually. In practice units can be chosen at the beginning of the session, and the need to change them later is not very frequent. Data saving feature When at the end of the session you exit CaLC3 by hitting F7, datafile calc3.dat is made. That file contains all the last values in CaLC3. When the program is started next time, those values are read in and one can continue from the previous situation. If no datafile is found, zeros are seen on the screen. EXAMPLES -------- The following examples demonstrate, how to use CaLC3 in common RF problems. Example 1 We have an electrically short GP antenna, which is loaded with a serial coil to get it resonate at 3.7 MHz. We measure its feed- point impedance, and find 20 ohm + j 0 ohm at that frequency. Now we would like to feed the antenna with 50 ohm coax and use a simple LC-match between the antenna and the feed line. The values for coil and capacitor must be calculated. We activate Impedance section and put Rs = 20 ohm. Then we begin to increase Xs watching the value of Rp going upwards. After some trials we get: 20 ohm + j 24.5 ohm = 50.0 ohm // j 40.8 ohm Alternatively by trying negative Xs values we get: 20 ohm - j 24.5 ohm = 50.0 ohm // -j 40.8 ohm We choose the low pass version putting a coil of 24.5 ohm at 3.7 MHz in series with the feed-point and compensating the equivalent 40.8 ohm inductive shunt reactance with a parallel capacitor at the high impedance side. For inductance and capacitance values we shift to fLCX and find that at 3.7 MHz 24.5 ohm corresponds to 1.05 uH and 40.8 ohm to 1.06 nF. Example 2 In the ARRL UHF/Microwave Experimenter's Manual 1990 on page 8.30 there is shown a series/parallel conversion example using measured s11 for NE021 at 2 GHz. We consider input match. Input and output s-parameters s11 and s22 can be transformed to any presentation of complex impedance. This has been done traditionally on Smith Chart by locating the point where reflection coefficient equals s11 of the device and reading the complex impedance corresponding to that point. The same can be done using Impedance calculation by putting the magnitude to gamma line (8) and phase to phi line (9). Zo must be right, normally 50 ohm. We find that 0.49 /_108 deg equals 24.63 ohm + j 30 ohm. in parallel form 61.67 ohm // j 50.28 ohm. We find also that with no input matching at all return loss at the input is 6.2 dB, which lowers the total gain by 1.2 dB. From the parallel form of input impedance we see, that quite good match can be achieved at 2 GHz just by placing a 50 ohm capacitive reactance over the input. From fLCX we get 1.59 pF for the capacitance value. We wonder, if a lumped chip capacitor would be OK. Because of the high operating frequency the series inductance of the capacitor must be considered. Going to Cs + Ls we check the effective capacitances at 2 GHz for 1p0 and 1p2 chip capacitors. We assume, that Ls is 1.3 nH. For effective capacitances we get 1.26 pF for 1p0 and 1.59 pF for 1p2. We choose 1p0 thinking it to be best not to complitely cancel the inductive Xp to be able to lower the resistive part some what by a low value block capacitor, which is needed anyhow. We return to fLCX and find that 1.26 pF corresponds to 63.16 ohm at 2 GHz. Then we solve the total reactance of the parallel connection of -j 63.16 and +j 50.28 ohm. Using X1 // X2 we get +j 246.6 ohm. Now we have the parallel impedance seen towards the input of NE021 with 1p0 chip capacitor coupled over it, 61.67 ohm // +j 246.6 ohm. We put this parallel impedance into Impedance and get the series form 58.04 ohm +j 14.51 ohm. We read input RL is 16.4 dB and mismatch loss 0.1 dB. We now check a capacitor value for 14.5 ohm, and find that 2.7 pF with 1.3 nH in series will have -j 13.1 ohm at 2 GHz. Theoretically cancelling the series inductance would improve the input match to RL 22.6 dB. This example is good in the respect, that it shows the effect of capacitor's series inductance, but simplified in the respect that the effect of microstrip lines was not considered. Also interaction between input and output of the device was thought to be small. And best NF not necessarily coincides with the best power transfer. Example 3 We need a booster amplifier to a 2 m walkie talkie. We have a 25 W VHF transistor in a drawer, and Philips, the manufacturer states that its input impedance at 144 MHz is 1.7 ohm + j 1.4 ohm. We start designing input matching circuit and find that this problem is much like the two examples above. Example 4 This example shows, how to figure out a practical improvement to a simple low-pass filter. We have made a 20 meter TX, and find that harmonic emissions are horribly high and need a harmonic filter to be inserted in the feed-line. We start with a the following pi-filter: C1 = 200 pF L = 550 nH C2 = 200 pF It has good match at 14.2 MHz, but attenuation at second and third harmonic frequency is not high enough: 28.4 MHz: - 8.0 dBc 42.6 MHz: -19.3 dBc We would like to improve harmonic attenuation by introducing series inductance to capacitors to resonate them at the harmonic frequencies. The problem is to find the proper combination of LC, which yelds resonance at the harmonic frequency and represents a 200 pF capacitor at the working frequency 14.2 MHz. We don't have to know the exact reactance of 200 pF at 14.2 MHz at this phase. We activate Ls + Cs, set f to 14.2 MHz and begin to lower Cs from 200 pF downwards at practical steps varying Ls to find a combination, where Ct = 200 pF and fr = 28.4 MHz for the notch at second harmonic. For third harmonic we look for Ct = 200 pF and fr = 42.6 MHz. In practice we increase Ls untill fr is right. If then Ct is too high, Cs must be decreased. We get values: Cs1 = 180 pF Ls1 = 68 nH Cs2 = 150 pF Ls2 = 210 nH Now if we look the frequency response with an RF circuit analysis program, we find notches at the harmonic frequencies as calculated, and no noticeable change in the pass-band. Cp // Lp can be used in a similar way in replacing L in the circuit with a parallel LC to get high attenuation at a particular frequency. If we scale this filter to 144 MHz, we will find that the series inductances just calculated mean control of lead lengths when ordinary ceramic capacitors are used. Example 5 CaLC3 is useful in analyzing circuits in impedance domain. A piece of paper and a hand calculator is needed for additions and substractions. Take the previous filter example. Starting backwards from the load the end of the inductor L sees C2 in parallel with the load, 50 ohm // 200 pF. fLCX: 200 pF at 14.2 MHz equals -j 56.04 ohm Impedance: Rp = 50.00 ohm Xp = -56.04 ohm we get: Rs = 27.84 ohm Xs = -24.84 ohm fLCX: 550 nH at 14.2 MHz equals j 49.07 ohm We sum -j 24.84 +j 49.07 = +j 24.23 The high point of C1 sees 27.84 ohm + j 24.23 Impedance: we get: Rp = 48.93 ohm Xp = 56.22 ohm Generator sees C1 in parallel with this impedance We use X1 // X2 to find that +j 56.22 // -j 56.04 = -j 17500 If we now put into Impedance 48.93 ohm // -j 17500 ohm, it equals 48.98 ohm -j 0.14 ohm. We see that return loss is 39.2 dB, which is a pretty good match.

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