## Capacitance Measure

### CIRCUIT

##### DMM_CAP_MEAS1.CIR
Download
the SPICE file

A quick search on "capacitance measurement" reaps a variety of intersting and clever methods. But the real challenge is choosing the method that takes advantage of your exisiting circuitry for other functions.

Folloowing the design of the Fluke meter, we see how the dual-slope integrator can be leveraged for the measurement of capacitance. Basically, the integrator will be used to find the total charge Q needed to bring the capacitor's potential up to a referelce voltage Vc.

### CAPACITANCE

The unknown capacitance (Rx) is defined by the charge Q accumulated on it's plates and the voltage Vc across it's terminals.

### HOW MUCH CHARGE?

We can't measure the charge directly. However, we do know that integrating the current over time, gets us the total charge.

How do measure the instantasneous current? Notice there's a sense resistor Rs inseries with the C.

Vs = i · Rs.

### THE METHOD

Basically, we'll charge up the capacitor to a reference voltage Vc and simultaneously measure how much charge it took to accomplish this. The capacitance is calculated as C = Q/Vc.

How is this performed? **During T1, switch SC1 closes and the capacitor C
charges to Vc**. The voltage across the Rs is fed to the dual-slope integrator
via S1. Notice the polarity of the diff amp is -1.0 such that -Vs feed the
inverting integrator thereby developing a positive voltage at Vo.

**During T2, the reference voltage Vref is fed to the integrator via S2 and
the integrator ramps down to 0V**. (Meanwhile the capacitor is discharged
through SC2).

Because the integrator ramps up and down equally, you can set V1=V2. You'll immediately notice that the R1 and C1 terms cancel leaving you with

Solving for Q you get

Q = Vref ·T2 / Rs

The last piece of the method is calculating capacitance from charge.

C = Q/Vc = Vref ·T2 / (Rs·Vc)

Awesome sauce! In terms of the meter's reading, the interval T2 is propoertional to the measured capacitance.

T2 = (C·Rs·Vc) / Vref

### MEASURE IT

We'll let the rubber meet the pavement with an example. Choosing Vc=10V, Vref=1V, Rs=1k and T2=10ms max, what is the full scale capacitance we can measure?

C = Q/Vc = (Vref ·T2) / (Rs·Vc) = (10V·10ms)/(1k·1V) = 1uF

This equation tells that **the interval T2 (0 to 10ms)
represents the measured capacoitance (0 to 1uF). **Initially, set the
unknown capacitance to CX=1uF.

voltage V(22), integrator output V(3) and comparator output V(5). Note
that the falling edge of V(5) at Tfall indicates the end of
T2.

= Tfall - 10ms

For CX=1uF ohms, where is the falling edge of V(5)? Uing the cursor, you find Tfall = 19.01ms which implies T1 = 20.003-10.0 = 10.003ms. The capacitance is easily calculated as

= T2 /10m · 1 uF

= 1.0003 uF

A reasonable measuremnt of capacitance!

Try entering another value of Cx. Rerun the simulation and check your result. What happens when the Cx gets too smalll? Try measureing Cx near 0.1 or 0.01 uF. How accurate is the measurement? Might be best to switch to lower range. What value of Rs is needed for these values? Did the accuracy improve?

DMM SERIES

Measure DC Volts with a Decade
Resistor Resistor Network.

Measure DC Current with a Decade
Current Sense Resistor Network.

Measure Resistance with a simple
modification of the Dual-Slope Integrator.

### SPICE FILE

DVM_CAP_MEAS1.CIR * * CHARGE AND DISCHARGE C VC 20 0 10VDC SC1 20 21 15 0 SWB SC2 21 0 15 0 SWA * * RS - CURRENT SENSE RS 21 22 1000 * * CX - UNKNOWN CAPACITOR CX 22 0 1UF * * VREF VREF 25 0 1VDC * * DIFF AMP - V REF E_DIF2 12 0 25 0 +1.0 * * DIFF AMP - RS E_DIF1 11 0 21 22 -1.0 * * CONTROL: VCNTRL=0 S1=ON, S2=OFF * VCNTRL=1 S1=Off,S2=ON VCNTL 15 0 PWL(0MS 0V 10MS 0V 10.01MS 5V) * * INTEGRATOR S1 11 1 15 0 SWB S2 12 1 31 0 SWA R1 1 2 100K C1 2 3 0.10UF IC=0V XOP1 0 2 3 OPAMP1 * * COMPARATOR (ZERO CROSSING DETECTOR) XCMP1 3 0 5 COMP1 * * AND GATE, S2 = ON IF VCNTRL AND XCMP1 OUTPUTS ARE HI VCC 30 0 DC 5V R31 30 31 10k D31 31 15 D1N4148 D32 31 5 D1N4148 * * * SUBCIRCUITS AND MODELS *********************************** * .SUBCKT COMP1 1 2 5 * TERMINALS: 1-INPUT+, 2-INPUT-, 5-OUTPUT * DIFF AMP EDIFF 3 0 VALUE = { V(1) - V(2) } * FREQUENCY RESPONSE RP1 3 4 500 CP1 4 0 1000PF * LIMITER EOUT 5 0 TABLE {V(4)} = (-0.5MV 0V) (0.5MV, 5V) .ENDS * * * OPAMP MACRO MODEL, SINGLE-POLE WITH 15V OUTPUT CLAMP * connections: non-inverting input * | inverting input * | | output * | | | .SUBCKT OPAMP1 1 2 6 * INPUT IMPEDANCE RIN 1 2 10MEG * DC GAIN=100K AND POLE1=100HZ * UNITY GAIN = DCGAIN X POLE1 = 10MHZ EGAIN 3 0 1 2 100K RP1 3 4 100K CP1 4 0 0.0159UF * OUTPUT BUFFER AND RESISTANCE EBUFFER 5 0 4 0 1 ROUT 5 6 10 .ENDS * .MODEL SWA VSWITCH(VON=5 VOFF=0 RON=1 ROFF=1e12) .MODEL SWB VSWITCH(VON=0 VOFF=5 RON=1 ROFF=1e12) * * DIODE .model D1N4148 D(Is=0.1p Rs=16 CJO=2p Tt=12n Bv=100 Ibv=0.1p) * * ANALYSIS ************************************************* .TRAN 25US 21MS UIC *.TRAN 0.1US 2000US UIC* .PROBE .END