Electronics
Frequency-response calculation software

# Frequency Response of Wire-End-Resistors and Small VHF Choke Coils

Author: R.J.Edwards G4FGQ © 18th July 2005

This program calculates the frequency-response of resistors and small chokes. The resistor model circuit used by this program

La= Series inductance of connecting wire
Lc = Inductance of metal film resistance spiral
R = DC resistance of spiral element
Ca = Capacitance-to-ground of resistor connecting wire
Cc= Capacitance-to-ground of resistor spiral element

L and C values are estimated from a component's dimensions. The program calculates the input impedance, Zin, of a resistor or small VHF choke versus frequency with the other end grounded. Behaviour is analysed as a radio transmitter's RF dummy load.

Assumptions

• The two connecting wires have equal lengths.
• The diameter of the connecting wires is 0.75 mm.
• The clearance between a resistor and a ground plane is half the diameter of the resistor body.

Notes

• For carbon and similar rod resistors enter zero spiral turns in the program.
• For single-layer wound VHF chokes enter a few ohms for winding wire resistance.
• Resistors of several hundred ohms make better wideband dummy loads than resistors with lower values. For low value, higher power, dummy loads, connect higher value resistors in parallel for optimum performance. Avoid series connected resistors because of their higher combined inductance.
• The inductive reactance component of Zin causes much more performance degradation versus frequency than the simple impedance deviation of Zin from Zo.
• A dummy load can be no better than the tolerance on the DC resistance value. For example, for a typical tolerance of 5% the reflection coefficient at high frequencies should be no greater than 0.025 or an SWR greater than 1.05.
• The behaviour is that of a short-circuited transmission line in the test circuit.

Start testing at a very low frequency. Then increase the frequency until a maximum input impedance is observed. This corresponds to a short-circuited quarter-wavelength of line. A further increase in frequency may result in a minimum input impedance which corresponds to a half-wavelength of line, and so on.

These resonances will not correspond exactly with the resistor's physical length because the line's model consists of lumped T and L sections and the resistor itself does not have uniformly distributed values of L, C and R.

The higher frequencies are included in the program to illustrate what actually happens at VHF and UHF. However, resistors of this type have little useful value at high frequencies where the reflection coefficient exceeds 0.1 or the SWR exceeds 1.2 or 1.3.

The angle of the reflection coefficient is included in results as it may be useful in further calculations of circuit performance.

The SWR is included because the resistor may terminate a long transmission line of impedance Zo and cause standing waves. Otherwise the SWR has no meaning.

VHF choke coils can be single-layer-wound on high-value resistor bodies. Losses in the resistor will lower choke resonance Q's and reduce the chance of parasitic oscillations where chokes are used in amplifying circuits.

Environment
The environment of a resistor has a large effect on its frequency response at very high frequencies. The effect increases indefinitely with frequency.

In this program resistors are assumed to be mounted above a ground plane on a circuit board. The spacing between the resistor body and the ground plane is one-half the diameter of the resistor body.

There may be other components on the circuit board. There may be a metal screen or shield above the resistor. All of which increases the uncertainty of the coupling and the stray capacitance between the resistor and its surroundings and between one end of it and the other. These factors therefore contribute some amount of performance randomness.

Nevertheless, circuit designers should have some idea of the effects of such uncertainties on circuit operation if only to set worst case limits of some kind at various operating frequencies and in different resistance ranges.

The program attempts to set limits on the magnitude of possible calculation errors in random situations. An impedance Z = Sqrt(Total inductance/Total stray capacitance) will be computed. It will be noticed that at DC resistance values two or three times Z the errors tend to decrease. Vary the DC resistance while keeping frequency constant. The most reliable output data occurs at RC < 0.1 and SWR < 1.2.