Determine a cable core diameter for RF current carrying loop

[Bhushan]

Basic Question Alert ! (I need to brush up my basics and need your help)

Problem Statement: I wish to make a current carring cable loop to generate a controlled magnetic field. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html

As I understand, the magnetic field generated depends on the Current in the loop and Loop radius (Fixed). I wish to maintain the current in the 50ohm loop to 25.3mA and 8mA respectively (ie. we have voltage of 1.26V equivalent to 12-13dBm and 0.4V equivalent to 2-3dBm).

I have a signal generator which can only support max RF output level of 13dBm.

I wish to have a cable diameter as large as possible so that the resonance frequency of the loop is higher. The operating frequency is below 7MHz.

As I understand the choosing a cable with higher cross section reduces the resistance and increases the power consumption. How can I determine the maximum cable core diameter (ie. thicker cable) for the loop cable so that I can maintain specified current levels in the loop with existing signal generator?

 

[Babadag]

See-for instance:
https://en.wikipedia.org/wiki/Skin_effect

 

[tech99]

Basic Question Alert ! (I need to brush up my basics and need your help)

Problem Statement: I wish to make a current carring cable loop to generate a controlled magnetic field. http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/curloo.html

As I understand, the magnetic field generated depends on the Current in the loop and Loop radius (Fixed). I wish to maintain the current in the 50ohm loop to 25.3mA and 8mA respectively (ie. we have voltage of 1.26V equivalent to 12-13dBm and 0.4V equivalent to 2-3dBm).

I have a signal generator which can only support max RF output level of 13dBm.

I wish to have a cable diameter as large as possible so that the resonance frequency of the loop is higher. The operating frequency is below 7MHz.

As I understand the choosing a cable with higher cross section reduces the resistance and increases the power consumption. How can I determine the maximum cable core diameter (ie. thicker cable) for the loop cable so that I can maintain specified current levels in the loop with existing signal generator?

The easiest way of obtaining a field which is known is to use an untuned loop and rely on the reactance of the coil to control the current. In this case, the resistance of the wire will have only a small effect. If the generator is 50 Ohms and has an EMF of 2 x 1.26 = 2.52V then you need a total impedance of Z = V/I = 2.52/0.0252 = 100 Ohms. The required reactance can be found from the formula X^2 = Z^2 - R^2 = 100^2 - 50^2.
From a rather wobbly memory, such a reactance can be obtained by using about 3 turns of wire about 250mm diameter. Keep the turns spaced slighty to reduce stray capacitance and wire of about 2mm will be suitable.
To find the reactance, place a capacitor of, say, 100pF in series with the loop and see what frequency it resonates at. Then apply the formula for resonant frequency of an LC circuit. F = 1 / 2 pi SQT (LC)
Unless you want to obtain the strongest possible field, I think that for the actual experiment it is better to avoid a loop that is brought to resonance with a capacitor, as it creates difficulties on obtaining 50 Ohms.