501S42E9R1CV4E Datasheet, PDF (1/5 Pages) Johanson Technology Inc. – Q & ESR EXPLAINED A JOHANSON TECHNOLOGY PRIMER

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Q & ESR EXPLAINED
A JOHANSON TECHNOLOGY PRIMER
November 24, 2004
One of the most important parameters in evaluating a high frequency chip capacitor is the Q
factor, or the related equivalent series resistance (ESR). In addition to providing excellent
performing RF components, JTI strives to provide our customers with accurate and complete data.
Towards this end, a more detailed discussion of Q & ESR measurement issues follows.
In theory, a “perfect” capacitor would exhibit an ESR of 0 (zero) ohms and would be purely
reactive with no real (resistive) component. The current going through the capacitor would lead the
voltage across the capacitor by exactly 90 degrees at all frequencies.
In real world usage, no capacitor is perfect, and will always exhibit some finite amount of ESR.
The ESR varies with frequency for a given capacitor, and is “equivalent” because its source is
from the characteristics of the conducting electrode structures and in the insulating dielectric
structure. For the purpose of modeling, the ESR is represented as a single series parasitic element.
In past decades, all capacitor parameters were measured at a standard of 1 MHz, but in today’s
high frequency world, this is far from sufficient. Typical values for a good high frequency
capacitor of a given value could run in the order of about 0.05 ohms at 200 MHz, 0.11 ohms at 900
MHz, and 0.14 ohms at 2000 MHz.
The quality factor Q, is a dimensionless number that is equal to the capacitor’s reactance
divided by the capacitor’s parasitic resistance (ESR). The value of Q changes greatly with
frequency as both reactance and resistance change with frequency. The reactance of a capacitor
changes tremendously with frequency or with the capacitance value, and therefore the Q value
could vary by a great amount. See Equations 1 and 2.
Eq. 1 :
|Xc| = 1 / { 2 (π) (f) (C) } ; where |Xc| is the absolute value of the reactance in Ohms;
f is the frequency in Hertz;
C is the capacitance In Farads
Eq. 2 :
Q = |Xc| / ESR ; where Q is a dimensionless number meaning 'Quality Factor';
|Xc| is the absolute value of the reactance in Ohms;
ESR is the Equivalent Series Resistance in Ohms
Johanson Technology measures ESR and Q on a Boonton 34A resonant line. The capacitor
under test is resonated with an inductive line of an accurately characterized impedance and Q.
From the resultant data (the center frequency and bandwidth of the resulting peak), the Q, ESR,
and capacitance value of the device is output. This method is a long-standing industry standard
for the measurement of Q and ESR at RF frequencies. Since this method depends on the frequency
accuracy of a signal generator (which can be measured with extreme precision), the data taken in
this manner is quite accurate. As the ESR of modern capacitors goes ever lower, the accuracy,
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