# Voltage and Frequency Dependence on Resistors

- Posted by Tomáš Zedníček
- On March 6, 2021
- 0

**Voltage Dependence**

If we apply a voltage on a resistor it’s resistance will *drop* slightly in certain types. Therefore the resistance change is negative. The change per volt of applied voltage is called *voltage coefficient, VC,* and is expressed in %/V or better, μV/V. The coefficient is determined not only by the resistive material but also by the dimensions, i.e., the electrical field strength, and the time of applied voltage. Thus, MIL-STD-202, Method 309 prescribes measurements when the voltage is applied intermittently for less than 0.5 seconds. Two measurements is performed: the resistance (r) at 0.1 x rated voltage (V_{R}) and the resistance (R) at 1.0 x V_{R}. The voltage coefficient, VC, then is computed as:

If we disregard pure metallic resistive elements common values of the voltage coefficient are between –10 and –100 μV/V. *The* *voltage dependence is negligible for resistance values below 1000 ohms*.

An evident voltage dependence combined with AC voltages will cause distortion and a third harmonic attenuation.

**Frequency Dependence**

A resistor has a certain parasitic degree of both capacitance and inductance. Between the turns there is a certain capacitive connection. Inductance appears already in a straight lead, approximately 1 nH/mm of length but is amplified by the coil action from windings and spiraled patterns. In carbon composition resistors only capacitance emanating from the multitude of parallel current paths manifests itself.

Figure 1 shows the equivalent circuit being simplified to models for high and low resistance values.

*Figure 1: Examples of equivalent circuits for resistors in different degrees of simplification.*

The frequency dependence of resistance **decreases** if the resistors:

- have small dimensions.
- have a low resistance value.
- are of a thin film design. Even a thick film design is favorable.
- have as short a lead as possible, like SMDs.
- are geometrically even, i.e., without sudden geometrical changes along the resistor body.

How the frequency dependence may influence the impedance is shown in Figure 2

*Figure 2: Examples of frequency dependence as the ratio of AC impedance through DC resistance for some different resistor types:*

- Carbon composition, ¼ W, 1 MW.
- Carbon composition, ¼ W, 100 kW.
- Chip, thick film, EIA size 0603, 100 kW; c » 0.05 pF; L » 0.4 nH.
- Metal glaze or metal film, DIN size 0207, 100 kW; c » 0.4 pF.
- MELF, DIN size 0204, 10 kW.
- Chip, thick film, EIA size 0603, 10 kW; c » 0.05 pF; L » 0.4 nH.; Chip, metal foil, EIA size 1210, 10 kW.
- Chip, thick film, EIA size 0603, 1 kW; c » 0.05 pF; L » 0.4 nH.
- MELF, DIN size 0102, high frequency design, 10 W; c » 0.035 pF; L » 0.8 nH.
- MELF, DIN size 0204, 10 W.
- Chip, thick film, EIA size 0603, 10 W; c » 0.05 pF; L » 0.4 nH.
- Chip, thin film, EIA size 0603, 100 W; c » 0.035 pF; L » 1.2 nH.
- Chip, thick film, EIA size 0603, 100 W; c » 0.05 pF; L » 0.4 nH.

The examples in Figure 3 represent a guide only. They are taken from major manufacturers’ data sheet. Note how the resistance value of an otherwise equivalent component influences the parameters: No. 3, 6, 7, 10 and 12. Another example, No. 8, shows a MELF component that, by means of a specific spiraling technique, is given excellent high-frequency characteristics. Generally the *frequency dependence* of the different resistor materials can be divided into three groups:

### Different resistor materials

wdt_ID | Technology | Frequency Dependence |
---|---|---|

1 | Carbon composition | high |

4 | Metal glaze, cermet, thick film | moderate to low |

7 | Metal film, metal oxide and carbon film | low |

*Film resistors* may approximately be classified as follows:

- values < 100Ω are inductive.
- values between 100 and 470Ω are practically true resistive.
- values above 470Ω are capacitive.

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