RFC rel. 1.6 USER MANUAL written by Giorgio FONTANA Topics : 1) How to use RFC. 2) Examples. 1) HOW TO USE RFC. CONFIGURATION: RFC can be configured by editing the file RFC.CFG. RFC.CFG is an ASCII file which contains 10 lines, extra lines are not considered by the program. RFC.CFG must be in the directory of RFCxx.EXE and RFC.PIC. RFC.CFG contains the following information: The speed of light in Km/ms 299.792 The number of points per arc 20 (1 to 100 allowed) The data drive and directory (space or string like c: c:\rfc\ ...) The language switch E (E=english,I=italian,N=on line select) The keyboard autorepeat rate 0 (0 to 31, 32 disables, 0=fastest) The logout autorepeat rate 0 (0 to 31, 32 disables, 0=fastest) The palette color for Z map 1 (0 to 63) The palette color for Y map 2 The palette color for R map 4 The palette color for Q map 56 Comments RFC.CFG could be omitted obtaining: The speed of light in Km/ms 299.792 The number of points per arc 20 The data drive and directory same as RFC.EXE The language switch N The keyboard autorepeat rate 32 The logout autorepeat rate 32 The palette color for Z map 1 The palette color for Y map 2 The palette color for R map 4 The palette color for Q map 56 DEFAULT UNITS: ohm, mho, pF, uH, meters, dB/m, MHz, degrees, turn ratio (N) STARTING RFC: Once configured the program can be started typing RFC16. Now the summary of the commands is presented to you. The summary can be recalled later by the command . Please choose the characteristic impedance of the chart, which is the impedance that corresponds to the center of the chart, where the reflection coefficient is zero. Then choose the frequency. On the left side of the screen there is the complex plane of the reflection coefficient. A graphic cursor can be moved in the plane using the arrow keys. The impedance, admittance, reflection coefficient, and Q charts can be displayed using , , , . On the right side of the screen an info display shows the coordinates of the cursor in many equivalent forms. Press and

to get other equivalent quantities. The info display is linked to the cursor when the cursor is moved. The info display shows the start impedance when the start impedance is defined with or when a network is loaded from the disk. The info display shows the impedance at the end of the arc associated to the element selected by if is used. The info display shows the impedance at the end of the network if the element selected by is the last element of the network. HOW TO DEFINE THE START IMPEDANCE: The start impedance can be defined by moving the cursor to the start impedance and typing to set the impedance. A red square is placed around the cursor. The start impedance can be defined numerically with the key . You can choose among impedance, admittance, reflection coefficient and file. If you choose impedance or admittance, you are allowed to select an equivalent circuit RL or RC. If you do so, the start impedance is frequency dependent. The input file is named ####.inp. It is an ASCII file with the number of start points at the beginning, then the list of frequencies and impedances follows. . . . . . . . . . Ex: 4 120 45 12 130 48 -14 140 55 -20 180 70 -33 Using the file option the impedance as a function of frequency is linearly interpolated between the values written in the file. If the actual frequency is lower than the lowest frequency in the file, the actual impedance is the impedance that corresponds to the lowest frequency in the file. If the actual frequency is higher than the highest frequency in the file the actual impedance is the impedance that corresponds to the highest frequency in the file. The frequency list must be strictly increasing from the first to the last line. The maximum number of points is 200. Using the impedance selected can be outside the plane. HOW TO ADD ELEMENTS TO THE START IMPEDANCE: Elements can be added using . Elements L, C and Z can be added in series or in parallel to the preceding element. Element T (transmission line) can be connected as transmission line or stub. Element M (ideal transformer) can be connected as transformer with common grounds. Key <=> shows the schematic of the network. You can redefine an element by selecting it with then press . HOW TO TUNE AN ELEMENT: A couple of keys is associated to each element, see the Key field of the info display. Using the Keys (upper and lower case) you can trim the values of up to 2 parameters of the element: Element Upper case Lower case first parameter second parameter C capacitance L inductance Z resistance reactance T lenght characteristic impedance M turn ratio The info display shows the value of the last parameter that has been trimmed. All the parameters of an element can be displayed selecting the element with then press . HARDCOPY: prints the listing of the network and the hardcopy of the graphic display (big) or the hardcopy of the screeen (small). HP Laserjet and Epson formats are supported. AUTOTUNING: To reach a given impedance with your network, first choose the impedance with the cursor, then press <#>. Autotuning tunes the first parameter of each class of elements. An element can be locked using to select it and to lock and unlock. If the number of unlocked elements is >2 then the Q of the network is minimized too, but the procedure may not converge exactly to the desired impedance, to correct lock one or more elements. Autotuning works with a fixed number of iterations, sometimes it is necessary to call it more than once. MONTECARLO SIMULATION: starts a Montecarlo simulation for tolerance evaluation. Type the tolerance in +- xx% for the parameters required by the program and choose the number of simulations. The program shows the end impedances marked with green points. The numer of different points is shown in the info display. The area plot can be erased and recalled using <^>. FREQUENCY SWEEP: starts the frequency sweep. The plot can be erased and recalled using <^>. <^> : the buffer is preserved after the loading of a new network to compare the behaviour of two networks. Type <^> before performing the frequency sweep with the second network. To plot a frequency sweep type , then type the start frequency (low frequency), the stop frequency (high frequency), the frequency step, and the number of steps between markers. A green point is plotted every frequency step, while a green cross is plotted every a given number of frequency steps. CIRCLE DRAWING: To draw a circle move the cursor to the center of the circle and press , a green point shows the center of the circle. Then move the cursor to a point on the circumference of the circle and press again, a circle is drawn. Now the key erases and recalls the last circle drawn. HOW TO MARK A POINT: Move the corsor to the point and press . The same Key deletes the point. MOUSE OPERATION Exploring the plane is slow with the arrow keys. Using the mouse the cursor could be moved very fast. If no mouse button is pressed, the mouse control is uneffective and only the arrow keys are functional. Pressing the left button, the cursor can be moved with the mouse and also with the arrow keys. Pressing the right button the start impedance is set at the cursor position. Pressing both buttons the cursor and the start impedance can be moved together and the network is dynamically recalculated. CALCULATOR FOR COMPLEX NUMBERS: The key <$> recalls a calculator for complex numbers. The buffer of the calculator is ratained and saved with the network data file. Select the operation with <+>, <->, <*>, , , , select the field with , <\>, , enter a number with , NUMBER, , select the mode with <>> and <<> (modulus and phase (degrees) or real and imaginary parts). HOW TO SAVE A NETWORK ON DISK: Type and choose a six (maximum) digit code for the network. HOW TO RECALL A NETWORK FROM DISK: Type and type the code of the network. ONLINE SELECTION OF THE NUMBER OF POINTS PER ARC. Arcs are constructions that give a better feeling of the behaviour of an element of the network. Type to select a number of points between 1 and 100. The program is faster with few points per arc. HOW TO SELECT A NEW FREQUENCY: allows to select a new frequency. <-> and <+> can be used to step the frequency by 1, .1 or 10 MHz, the step depends on . HOW TO CHANGE THE STEP: changes the step for the tuning of the elements and frequency. At the beginning the step is 1 % and 1 MHz. The values are circled through .1%, .1MHz and 10% , 10 MHz. HOW TO RESET THE PROGRAM: resets the program. Confirmation required HOW TO QUIT THE PROGRAM: quits the program. Confirmation required 2) EXAMPLES 1) FIND THE COEFFICIENT OF REFLECTION OF A RC SERIES CIRCUIT. f=100 MHz, Zo=50 ohm, R=10 ohm, C=50 pF. SOLUTION: Start the program. Zo=50 Fo=100 10 50 Read the info. display and press and/or

to read different quantities. 2) MATCH A LOAD WITH REFLECTION COEFFICIENT .1905 ANGLE 324.55 TO 50 OHM RESISTIVE. Fo=188 MHz, USING A 50 OHM TRANSMISSION LINE AND A 50 OHM OPEN SERIES STUB. Zo=50 F0=188 .1905 324.55 .59 50 1 0 <0> .47 50 1 0 <1> <#> Press twice to read the end impedance. Find a better solution (using shorter lines). 3) FIND THE FREQUENCY PLOT OF A SERIES RLC CIRCUIT. Zo=50 Ohm, R=5 Ohm, C=10 pF, L= 1uH, F= 30 TO 60 MHz, step .1 MHz. Zo=50 Fo=50 5 10 1 ! 30 60 .1 Try <^> when finished. Find the resonant frequency of the circuit using <+> and <-> , type to reduce the frequency step to .1 MHz. (50.3 Mhz). 4) FIND THE FREQUENCY PLOT OF A TRANSFORMER WITH L1=1uH, L2=4uH, k (coupling factor)=.6 CONNECTED TO 50 Ohm RESISTIVE. f=1 TO 20 MHz. Using a simplified equivalent schema: k=M/SQR(L1*L2) M= K*SQR(L1*L2)=2*.6=1.2uH Ls=L1(1-k^2)=1*.64=.64uH Lp=k^2*L1=.36uH N=L2/M=4/1.2=3.33 Zo=50 Fo=10 80 .64 .36

3.33 <=> ! 1 20 .1 RFC is a CALCULATOR. The PHYSICS and ELECTRONICS of electromagnetic fields, waves and devices must be the background of RFC users. See for example: 'Foundation for microwave engineering' R.E. Collin - McGRAW-HILL. and 'ELECTRONIC APPLICATIONS OF THE SMITH CHART' P.H. Smith, copyright by Analog Instruments Co., New Providence, N.J.