 Helpful mathematics

I made the experience that many radio amateurs give up, if the first mathematical equation cropping. But that does not have to be. On this webpage I offer the calculation of simple circuits and other things from the range of radio amateurs as forms. Their use is easy, so each one can use it. If you want to know, how looks the equations used into the scripts, then see the mathematical background at the end of each webpage. Resistors In the meantime are resistors available of the series E24 and E96 with tolerance of 1 % relativ inexpensive. So the usuable 24 or 96 values in each decade, which have at one's disposal, should be sufficient for homebrewer. But if one need resistors with higher power dissipation or reduced tolerance, one can fall back only on resistors of other series. You can use the calculation to determine the nonexistent values, a calculation of parallel/series connections of up to 5 resistors series E12 are possible with a small javascript. Especially for attenuators "crooked" values are required, however, which can be conveniently calculated as parallel/series connections of 2 resistors series E24/E12. Especially circuits with many resistors in some cases can not be simplified through the parallel or series connection of resistors. The problem solves only the star-delta-transform. With the help of this transform at least a circuit part of 3 resistors can be so converted, that then a parallel or series connection of 2 adjacent resistors is possible. To come to a solution for the entire circuit, you may must apply the transform at different circuit parts and in different directions. The calculation of the star-delta-transform of resistors is possible with a small Javascript. If the output level of a stage is too high, in order to be led directly to the input of another, one scolded attenuators between them. The calculation of attenuators is possible with a small javascript.
But only rarely resistances are available in the computed values. Change on the specified page the calculated resistances against from you used and see, which deviations with it to arise.
If larger power must be processed, you can use the calculation of power attenuators to determine additionally the necessary power dissipations for individual resistors. At the attenuators were used so far, the input and output impedances are equal. However if different impedances must be adapted somehow, it can be also used resistors for it. The calculation of the loss arising inevitably with it determine the calculation of attenuators with minimum loss.
Since no coils or capacitors are used in the 3 circuit above, the matching takes place frequency-independently. Attenuators are suitable therby for the wide-band matching. Sometimes it is necessary to divide an output signal on several building groups. Also this is realizable with resistors. The calculation of the loss arising inevitably with it determine the calculation of signal splitters. Since no coils or capacitors are used, the matching takes place frequency-independently. Attenuators are suitable therby for the wide-band matching. Mechanical small resistors are provided with a code in the form of color bands. For resistors with 3 or 4 color bands, the first 2 color bands denotes the value. The third color band denotes the multiplier and the 4. color band denotes the tolerance. For resistors with 5 color bands, the first 3 color bands denotes the value. The fourth color band denotes the multiplier and the 5. color band denotes the tolerance. You can ascertain with the color code calculator for resistors the value and tolerance.  Capacitors Capacitors are available with twelve values per decade. However sometimes values are required, which are not produced as norm values. You can calculate the value of the capacitor, which results from the parallel or series connections of up to 5 capacitors. A variable capacitor is rather rarely directly applicable in a circuit. If the tuning range is too largely and/or the initial capacity is too small, the desired values can be reached nevertheless by 2 additional capacitors. Frequently this is used as so called band spread in a VFO. You can use the calculator of the band spread. But only rarely capacitors are available in the calculated values. Change on the specified page the calculated capacitors against from you used and see, which deviations with it to arise.  Reactances Every now and then resistors must be connected. With ohmic resistors the calculation is simple. The calculation of parallel and series connection of reactances is a little more difficult, but possible under the same rules. With it you can calculate reactances with 2 coils, 2 capacitors or one capacitor and one coil. The components can thereby also contain resistive components. Each reactance consists an ohmic resistor. Capacitive reactances additionally include a capacitor and inductive reactances include a coil. Each series of complex resistances can be replaced by an electrically equivalent of a parallel reactances and vice versa. The conversion of reactances in series and parallel connections is possible with a small javascript. Each capacitor and each coil has a frequency-dependent reactive resistor (reactance). Conversely, the corresponding component can be calculated from any reactive resistor (reactance) at a given frequency. The calculation of reactances is possible with a small javascript.  Resonant circuits and LC networks Important elements are coils and capacitors, particularly if they appear together as resonant circuit. The calculation of resonant circuits determine mutually the frequency, the inductivity and the capacity of a tank circuit. By the way also the impedances of the circuits will be calculated. That are equal to the inductive reactances of the coils and to the capacitive reactances of the capacitors. The Austrian radio amateur named Josef Fuchs, OE1JF, used for matching of ½ λ dipoles at its ends a resonant circuit (Fuchs network). The calculation of Fuchs networks is possible with a small javascript, based on the finite impedance at the antenna ends an the used frequency. Such networks with coils and capacitors are usable only for one frequency. Circuit groups with different resistances can be connected with less loss over a coil and a capacitor. The values of the LC networks determined with the calculation of match of resistances are valid always only for one frequency, since the used parts are frequency-dependent. But it is not necessary, lest the output resistor is a resistance. It can be also a reactance. The script calculate only LC networks with low-pass characteristic. Such LC networks are in use in antenna tuners. The values of the LC networks determined with the calculation of match of reactances are valid always only for one frequency, since the used parts are frequency-dependent. Conversely, the calculation of antenna reactances is possible on the basis of the values of an antenna tuner.  Power and voltage

On this page, level data in watts (W), decibels based on 1 mW (dBm) and volts (V) at 50 Ω can be converted into each other.  Locator, distance and direction

One can convert a locator in the geographical latitude and longitude and versus. It's also possible to calculate the distance between 2 places on earth is possible, if you know the geographical latitude and longitude of both.  Heatsink All electronic components generate heat which must be dissipated in order do not to destroy it. In some cases the surface of the device itself is sufficient, in some other cases an additional heatsink is required. A few technical data are taken from the datasheet and the ambient temperature are only requires for the calculation of the thermal resistance of a heatsink. Thereafter, you can select a suitable heatsink from the assortment of electronic traders.  Keying speed

With a small Javascript you can convert the different data for the keying speed (words per minute, letters per minute, dots per minute or dot length in milliseconds) into each other. Only the knowed value must be marked. Next all other values are displayed.  Antenna The dimensions of multiband antennas such as the W3DZZ, the ZS6BZW or, more generally, a doublet antenna can also be calculated with a small javascript. This way you get to a tailor-made multi-band antenna, which does not necessarily have to have large dimensions.