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.


	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

	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

	     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

	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.


	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

	If no datafile is found, zeros are seen on the screen.


	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

	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
	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

		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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