Motivation:
Our idea is to realize an L-C-R meter which can measure the values of the basic electronic components Resistor(R), Capacitor(C) and Inductor (L) based on their basic governing equations viz.,
V=i*R for the Resistor, i=C(dv/dt) for the Capacitor and V=L(di/dt) for the Inductor
This implementation is done by using driving circuits to form the electric bias for the component under test and generate the required signals for the operation of the driving circuit from the micro controller.
The currently used meter applies some test voltage across the terminals between which the component under test is placed, by measuring the current being drawn depending on the mode selected (Ls,Rs),(Cs,Rs),(Lp,Rp),(Cp,Rp), it calculates the value of the component accordingly. Also the currently used meter measures the value of the component only at a selected frequency. But the newly proposed meter measures the value independent of the frequency of operation just based on the respective basic governing equation of the component. As the required signals are being generated from a microcontroller, the cost of implementation of this circuit will be very less as it just uses basic driving circuits and microcontroller for measuring the value of the component.
Hardware
We can’t use a single setup to measure the values spanning wide range. So, the hardware is designed to operate in two modes:
1. Constant current mode: Used for measuring lower range values of the components and for larger range components, the voltage saturates. 2. 100K ohm pull up mode: Used for measuring the larger values and for smaller values, this mode gives less accuracy.
Mode selection is done through driving a “mode select” pin:
low(for constant current mode) or high (for pull up resistor mode).
1. Constant current mode: > This will be the default initial mode of measurement. In this mode, a constant current of 1mA is pumped through the component and the voltage across it is sensed. This (sensed) voltage which is the input to the ADC is actually a stepped down version of the actual voltage by 5x. This step down is done so that the max. voltage to the input of the ADC doesn’t exceed the rating of the Micro controller being used (which is 3.3v here for the Tiva LaunchPad board). > The value of the sensed voltage is used to find the value of the component inserted between the terminals.
<Circuit diagram of Constant current mode>
2. Pull up Resistor Mode: > In the constant current mode, components with large values gives voltage higher than the supply voltage in which case, the voltage being sensed saturates to a max. value. This is detected by setting a threshold limit and driving the mode select pin to high on which the DUT(Device under Test) gets pulled up to supply with a 100k Ohm resistor instead of a constant current source.
<Circuit diagram of Pull Up Resistor mode>
Both the modes are implemented by just driving the mode select pin high or low.
<Complete circuit diagram (of board 1)>
Measurement of Resistance
1. In constant current mode, the output value of the ADC is the 1/5th of the voltage across the resistor when 1mA is passed through it. So, back calculation gives the resistor value:
Resistance = (Voltage/Current)
Actual Voltage = (5*ADC sensed voltage(in digital form)*3.3)/4095.
Resistance = (Actual Voltage)/(Current = 1mA) = Actual voltage*1000 (in Ohms)
Hence, Resistance (in Ohms) = (5*ADC Output*3.3*1000)/ 4095
2. Pull up resistor mode: A large value of resistor when passed a constant 1mA current, gives a high voltage which on the ADC is sensed as the maximum of 3.3V (due to saturation). So, to find the values of large resistors, we start with the default constant current mode and we set a threshold appropriately to distinguish between the lower and higher values of the resistors so that we can change the mode automatically by driving the mode select pin high. In this mode, the value of the resistor is back calculated from the voltage sensed using the voltage divider equation:
Actual voltage = (5*ADC output*3.3)/4095
Resistor value in K Ohms = (Actual Voltage * 100)/(Supply voltage - Actual Voltage)
<Flow chart of the Resistance measurement>
Capacitance Measurement
In the constant current mode, when a constant current is pushed on to a capacitor, the voltage across it ramps up linearly. The slope of this ramp is measured by the sensing the voltage at a known sampling frequency. In the implementation, we have calculated the value of the slope by fixing the change in voltage (dV) to 200mV (that corresponds to actual change of 200mV*5=1V) and finding the time that the voltage takes to reach to that value which is the dt.
These values of dV, dt and known i (constant current of 1mA), when inserted into the basic governing equation of i=C(dV/dt) gives the value of C as
C=i/(dV/dt)
We are able to measure the value of caps ranging from 1uF to 100uF using this constant current mode.
The pull up resistor mode can also be explored to find the value of the capacitor to extend the above range wherein the capacitor value is given according to the exponential increase/decay of the voltage of the capacitor when connected to a constant supply voltage through a series resistor. Hence, the capacitor value can be found from the relation:
Voltage sensed on the capacitor at an instant of time t (from the time of turning on the mode) = Supply voltage (1-e^(t/R*C)) where R=100K Ohm which is being used in the pull up mode of the circuit and supply voltage is around 12V in the implementation that has been done. It can be changed to 15V too by using the corresponding adapter for providing the power supply to the circuit.
< Flow chart of Capacitor measurement>
Inductance Measurement
For the inductor, instead of pushing in a constant current, a constant voltage is applied on to the inductor which makes the current through it to rise. By measuring the slope of the rising current, and by inserting it into the basic governing equation of the inductor i.e.,
V=L(di/dt) gives the value of the inductor.
The constant voltage is provided through a Low Drop voltage regulator (LDO) and the current is sensed by measuring the voltage across a low resistor (of around 7Ohm). (Refer to the circuit diagram) As the drop across this resistor would be very less, the output voltage of LDO can be very much approximated to that of voltage across the inductor itself which will be constant neglecting the drop on 7 Ohm resistor. This causes a ramp up of current in the inductor whose slope can be measured (in the similar way of measuring the voltage slope across capacitor earlier). The current in inductor is obtained by measuring the voltage across 7 Ohm resistor and dividing it by 7 to get the current in the inductor.
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