Device and method for measuring a value of a resistor
A device for measuring the value of a resistor has a first RC element with a first time constant and a second RC element with a second time constant. The first RC element has a first capacitor and a resistor. The second RC element has a second capacitor and the resistor to be measured. An evaluation circuit charges the first and second capacitors to a first and a second voltage, respectively, and initiates their discharge. The evaluation circuit measures the time that elapses from the start of the discharge to the instant at which the voltages across the capacitors are equal, and determines the value of the resistor from the values. In the event that the first time constant is larger than the second time constant, the first voltage is smaller than the second voltage, and vice versa.
1. A method of measuring a value of a resistor, which comprises:
providing a first RC element, formed of a first capacitor and a further resistor and having a first time constant, and charging the first capacitor to a first voltage;
providing a second RC element, formed of a second capacitor and the resistor to be measured and having a second time constant, and charging the second capacitor to a second voltage;
if the first time constant is greater than the second time constant, the first voltage is smaller than the second voltage, and vice versa, and a ratio of the first voltage to the second voltage is 1/K;
with an evaluation circuit, initiating a discharge of the capacitors and measuring a time interval that elapses from a start of the discharge of the capacitors to an instant at which the first and second voltages across the capacitors are equal, and determining a value of the resistor to be measured from the values of the first and second capacitors, of said further resistor, the ratio of the first voltage to the second voltage, and the measured time;
wherein said evaluation circuit is configured to determine the value of the resistor according to the formula
R
L
=
1
C
L
T
0
R
R
C
R
T
0
+
R
R
C
R
ln
K
wherein:
R L is the value of the resistor to be measured;
C L is the capacitance of the second capacitor;
T 0 is the measured time interval;
R R a resistance of the first resistor;
C R is a capacitance of the first capacitor;
K is a ratio of the first voltage to the second voltage.