# Resistor I-V Linearity

One most likely doesn’t need any assistance in recalling Ohm’s law as,

$$V = I R$$

Or equivalently,

$$I = \dfrac{V}{R}$$

Of course this is an idealized expression, as all resistors have a voltage coefficient due to self-heating. A resistor R will dissipate a power under load of

$$P_d = I^2 R$$

The power dissipation leads to a temperature rise and the temperature coefficient of resistance material leads to a deviation in nominal resistance.

In this blog post, we will take a look at the I-V linearity of a handful of 1 kOhm resistors.

Based on stock at hand, the following 1 kOhm resistors will be studied:

(A) Axial Metal Film (MFR-25FBF52) – 1/4 W
(B) Axial Carbon (CF14 1K 5% R) – 1/4 W
(C) Thick Film 0805 (RC0805JR-101KL) – 1/8 W
(D) Thick Film 0402 (RC0402JR-071KL)- 1/8 W
(E) Cermet 10 Turn Trimmer – 1/2 W
(F) Axial Carbon – 1 W

## Measurement Setup

All 6 DUT resistors can be seen mounted on a single-side FR4 board in the image below.

A voltage source Vs1 is programmaticly stepped from 0 to 20V in 100 mV steps. Ammeter Am1 measures the DUT bias current. Voltmeter Vm1 measures the potential across the DUT resistor.

## Measurement Results

Results of First Order Fit of I-V Curve
DUT ID Type $$R_{fit}$$ $$[\Omega]$$
(A) Axial Metal Film 997.56
(B) Axial Carbon 998.14
(C) Thick Film 0805 1007.11
(D) Thick Film 0402 979.15
(E) Trimmer 1050.15
(F) Axial Carbon 1043.95

Deviation of Nominal Resistance at Full Rated Load
DUT Type Pd Max [mW] $$\Delta R$$ $$[\text{ppm}]$$
Axial Metal Film 250 -564
Axial Carbon 250 9677
Thick Film 0805 125 -310
Thick Film 0402 125 -514
Trimmer 500 -100
Axial Carbon 1000 30000 (3%)

## Discussion

No consideration was given to thermal EMFs generated during tests. It was assumed thermal gradient from resistance element to hookup leads was matched from both resistor terminals (nulling emf errors).

The 2 surface mount 1 kOhm resistors have far lower thermal resistance from their resistance element to PCB (leadless parts).

Random deviations in the linearity plots for low bias voltages  is attributed to measurement noise of the 34401A (100 nArms precision).

The surface mount and metal film resistors continued to have equivalent linearity well being overdriven.

## Raw Data

The I-V curves collected for the 6 DUTs can be found as csv files below:

Files are formatted as,
DUT Voltage [V], DUT Current [A]

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