Protek 9216A - Background on Components and Measurements; Definitions of Resistive and Reactive Parameters; Component Categories

4
Background on Components and Measurements
Properties of Resistors, Inductors, and Capacitors
The measurements made by the 9216A Digital LCR Meter are based on the definitions of
impedance and the properties of discrete components designed to provide impedances
in electronic circuits.
Definitions of Resistive and Reactive Parameters
Let the sinusoidal voltage and current in an electronic circuit at a particular frequency f be
represented in the complex or phasor notation, given respectively by
 
v
tVtV   cos||)(
(1a)
 
 
tj
jtj
eeVeV
vv


|||| 

(1b)
 
i
tItI   cos||)(
(2a)
 
 
tj
jtj
eeIeI
ii


|||| 

(2b)
where
1j
,   2 f, and
v

and
i

are symbols for phases of the voltage and cur-
rent relative to the frequency f. The impedance of a circuit component is defined as the
complex number Z, in ohms, that gives the ratio of the voltage across the component to
the current in the component:
 
 
 
 
iv
i
v
j
tj
tj
e
I
V
eI
eV
tI
tV
ZZ








||
||
||
||
)(
)(
(3)
Component Categories
From equation (3), we observe that if the phases of the voltage across the component
and the current in it are equal, then the impedance is a real number:
 
||
||
||
||
0
I
V
e
I
V
Z
j

(4)
In this situation, the impedance is purely resistive, as an ideal resistor would be.
If the phase of the voltage is 90 degrees (/2 radians) ahead of the phase of the cur-
rent, then the impedance is a positive imaginary number:
 
||
||
||
||
2/
I
V
je
I
V
Z
j


(5)
Chapter
1