AIM Q-Measuremenat.pdf

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Q Measurement with the AIM4170
revised 7-22-08
Summary:
The AIM4170 can be used to determine the Q of coils and of tuned circuits.
A function is included in the program to measure the Q of series and parallel tuned
circuits. The Q of coils can be determined by noting the ratio of the reactance to the series
resistance at any frequency. Q values up to 200 can be measured accurately. A new
feature of a future update to the AIM program will be an option to plot Q versus
frequency. This is illustrated in graphs in this application note.
The AIM4170 is primarily an instrument for measuring impedance. In addition to its
application to antennas, it can also be used to measure components like resistors, coils,
capacitors, crystals, resonators, and transformers. The impedance characteristics can be
plotted over a wide range to see the effect of frequency.
This application note will show examples of how to use the AIM4170 to measure the Q
of coils and tuned circuits and also how to evaluate transformers. The concept of Q
(“Quality Factor”) relates the loss in a component to the amount of energy stored in the
component. Both coils and capacitors store energy but some of this is lost during each RF
cycle. The higher the Q, the lower the loss.
There are many different configurations for making coils with special properties for
different applications. The AIM makes it possible to study the effect of frequency on
various designs to see which coil is better for a particular application.
Toroidal coils are especially interesting to measure with the AIM because they are so
frequency dependent. They are quite useful because they allow much higher inductance
to be obtained in a smaller volume than a plain air coil. Also, the magnetic field is more
closely confined inside the core so there is less interaction between the coil and nearby
components. The core material used has to be selected with the frequency range in mind.
The AIM can show at a glance if a coil will be appropriate for a particular frequency
band. Small construction details, like the turn spacing around the toroid can be evaluated
quickly. The AIM can also be used to evaluate large impedances, like the common mode
impedance of baluns, which may be several Kohms.
Links:
www.w7zoi.net/coilq.pdf
- “Experiments with Coils and Q-Measurements” - by Wes
Hayward.
www.g3ynh.info/zdocs/magnetics/index.html
- numerous articles on coils
Some key words related to coils that you can look for with Google are:
Brooks coil – maximum inductance for a given wire length.
Rooks coil – coils with lower capacitance.
Wheeler’s formula – equations for calculating the inductance of air core coils.
Litz wire – special wire to reduce coil loss due to skin effect.
Wire gauge awg – general information on wire gauges and properties.
Larry Benko, W0QE, one of the AIM beta testers, has compared Q measurements made
with the AIM4170 to the HP4342 Q-meter with good results up to about 200. For Q’s
greater than 200, the AIM is not as accurate, but the general trend in Q is useful for
comparing coils. Larry has found that tuning out the inductive reactance with a high Q
capacitor (air dielectric) gives good correlation with the HP4342 for Q’s over 500. The
AIM’s Q measurement function can be used directly to measure the circuit Q at the
resonant frequency.
For more information on the AIM4170, check this website:
http://www.w5big.com/
Two of the coils used for this experiment:
Coil A:
#6 wire, 8 turns, diameter=2.65 inches length=2.4 inches
Inductance=3.1 uH (calculated) = 3.0 uH (measured)
Self-resonant freq = 54.4 MHz (calculated) = 48.6 MHz (measured)
Coil B:
#12 wire, 15 turns, diameter= 1.45 length=1.50
Inductance=5.5 uH (calculated) = 5.0 uH (measured)
Self-resonant freq = 54.4 MHz (calculated) = 44.9 MHz (measured)
When measuring the self-resonant frequency of coils, the equivalent capacity may be
very small. Placement of the coil and the AIM on the bench with respect to other
objects may affect the resonant frequency by a large percentage.
The inductance was calculated using Wheeler’s formula:
Inductance (uH) = Diameter
2
x NumTurns
2
/ (18 x Diameter + 40 x Length)
The self-resonant freq is calculated by the formula:
Self-Resonant_Freq(MHz) = 1176x(Length/Diameter)
0.2
/
( NumTurns x Diameter)
(Dimensions in inches)
Q of Coil A vs frequency
Coil A self-resonant frequency is 48.6 MHz
Plot of Q vs frequency for Coil B
Coil B self-resonant frequency is 44.9 MHz

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