## Resistor matcher.

### Introduction.

This is simple circuit to match resistors to better accuracy than their rated tolerance ( it does not measure resistors - only match them ).
You can normally match resistors to around 10% of their rated tolerance ( i.e. you can match 1% resistors to within 0.1% ).
Matching resistors to much less than 10% of their rated tolerance is normally a waste of time as their long-term stability is insufficient. If you need better accuracy, buy better resistors.
The circuit is designed so it can match resistors to around 0.1% using a cheap 3½ digit AC-voltmeter with a 200 mV range.
It takes a few hours to build the circuit on strip-board.

### Schematic.

Fig.1: Schematic.

The circuit around U1 is a balanced wien-bridge oscillator with a clipped sine-wave output of around 13 V p-p at 100 Hz.
The conditions for oscillation are:
R3 ≤ R5 / 2 ( a little less ).
R7 = R3 + R5.
R6 = 4 * R4.
C3 = C4 or if C3 is connected across R6: C3 = C4 / 4.
R1 and R2 set the bias point - typically centered between the supplies.
The frequency is: 1 / ( 2 * π * R4 * C4 )
The circuit should work with most general-purpose OP-AMPs that will run from a 9 V supply.
I originally built the circuit with a square-wave oscillator, but got erroneous readings with a low-cost multimeter due to an 5 V common-mode spike at each zero-crossing ( with a decent RMS voltmeter it works fine ).
R12..R15 is a reference divider for the bridge. You can use a 10-turn trimmer if you want, but I normally find 2 single turn trimmers in series easier to adjust.
Rs is the top resistor in the other half of the bridge, Rr is the reference resistor and Rt1..Rt18 are the "unknown" resistors.
Rs, Rr and Rt are all same value.
The 40-pin ZIF socket makes it easy to change resistors. These are very expensive, but you can often salvage one from a retired programmer ( or buy a cheap programmer and take it there ). The types that accept both 0.3" and 0.6" wide ICs are easiest to use. Note that you may have to increase the hole diameter in the board to 1.3 mm to fit the socket.
J1..J19 are pinrows with and a jumper or DIP switches.
Resistors should be 1% types, the 33 nF capacitors film types, the 10 nF capacitor a ceramic placed close to U1 pin 8 and the electrolytics should have a voltage rating of at least your supply voltage.

There is a limit to how low value resistors you can match with this circuit.
The available output current from the LM358 is around 10 mA setting a lower value for the resistors of around 1 kΩ.
The contact resistance in the ZIF socket and the switches will cancel if they are identical, but there is no way of guaranteeing that.
The contact resistance of the DIP switches I used is specified at ≤30 mΩ when new and ≤100 mΩ at end-of-life ( 2000 operations ).
I can not find any specification for the ZIF socket.
I measured both the DIP switch and the ZIF socket with a resistor lead in it and both were around 5 mΩ ( both are new ).
Expecting a maximum contact resistance difference of 100 mΩ around 1 KΩ seems to be a reasonable lower value for the resistors that can be matched.

If you do not want to build the oscillator, you can use a small wall mains-transformer with AC output instead. Simply connect it to the left-hand side of R10, R11 and leave all components to the left of R10, R11 out.

#### Matching resistors

Connect an battery-powered AC-voltmeter across the VOUT terminals and connect a battery.
Set the J1 DIP-switch to the on position, the rest to off.
Fill the socket with resistors ( or how many you want to test ). The resistors should be from the same tape. You will normally be able to find 2 or more resistors within 0.1% matching from a tape with 10 1% resistors.
Rs and Rr must be there. Rt1..Rt18 are the unknown.
Set R15 to its center position, adjust R14 to the minimum reading on the meter then adjust R15 for a more accurate minimum. This is close to 0 V or something is wrong.
Open J1 and close J2..J19 in turn. The resistor that gives the reading closest to 0 V is the best match to Rr.
If none of the Rt are close to 0 V, Rr is probably not typical for the tape. Swap Rs and Rr and repeat.

 VBR Rr, Rt difference VOUT / VBR VOUT 5 V 1% 0.25% 12 mV 5 V 0.5% 0.12% 6.2 mV 5 V 0.2% 0.05% 2.5 mV 5 V 0.1% 0.025% 1.2 mV 5 V 0.05% 0.012% 0.62 mV 5 V 0.02% 0.005% 0.25 mV 5 V 0.01% 0.0025% 0.12 mV

You can increase the output voltage by increasing the supply voltage. U1 will accept up to 30 V supply.
This will give a VBR of almost 20 V.

Fig.2: The finished tester. The empty IC-socket was the square-wave generator.

### Appendix A: Measurements.

This test was done to see how the setup works with a cheap ( €10 ) 3½ digit voltmeter.
The test was made with 20 resistors from a tape of 4.99 kΩ 1% metal film resistors.
I connected 2 meters in parallel over the the output and noted the reading for all 18 test resistors.
Then I took the 4 resistors that gave the best match on the low cost meter and measured them with a precision 4-wire ohm-meter.

 Resistor # Low cost meter Fluke 87 Resistor value Deviation from Rr Rr 0.1 mV 0.365 mV 5005.2 Ω Rt1 1.0 mV 1.273 mV Rt2 5.1 mV 5.214 mV Rt3 4.4 mV 4.394 mV Rt4 1.5 mV 1.577 mV Rt5 0.5 mV 0.870 mV Rt6 0.9 mV 1.167 mV Rt7 0.5 mV 0.832 mV 5006.3 Ω 0.022% Rt8 0.5 mV 0.957 mV 5007.7 Ω 0.050% Rt9 3.1 mV 3.223 mV Rt10 0.5 mV 0.828 mV 5005.1 Ω 0.002% Rt11 0.5 mV 0.816 mV 5006.0 Ω 0.016% R112 0.7 mV 1.048 mV Rt13 0.9 mV 1.189 mV Rt14 0.8 mV 1.125 mV Rt15 0.7 mV 1.079 mV Rt16 2.8 mV 2.878 mV Rt17 3.9 mV 4.001 mV Rt18 1.6 mV 1.778 mV

The low cost meter is more difficult to read than the Fluke meter as the lower digit changes with 2..3 counts. The reading is an estimate of an average.
Another issue with this meter was that it overloaded when the switches were changed so I had to wait 20..30 seconds for a reading. D2 and D3 is a fix for that.
The Fluke meter is a lot easier to read as it has an average function.
I do not know what the absolute accuracy of the ohm-meter is as it has not been calibrated recently, but the relative values should be accurate.
I got 6 pairs matched to within 0.1% out of the 20 I used for this test.

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