# Output resistance

The output resistance R i , also referred to as internal resistance or source resistance , characterizes the output of an electronic component, an assembly or a device when the load changes. There is no uniform value because:

• The differential resistance is decisive for slow, small load changes
• In the case of rapid changes, the dynamic internal resistance is important
• The maximum current is determined with the static internal resistance.

Only in the rarest of cases do all three results agree. A measurement with an ohmmeter is usually impossible. When it comes to complex resistances that also contain inductances and capacitances, the so-called output resistance is an output impedance .

## Causes of internal resistance

### Static internal resistance

In every electrical device, the current runs through copper wires that contribute to the internal resistance. In a dynamic microphone it can be 200 Ω, but only 0.01 Ω in a power transformer. In batteries , the current runs through conductors with much poorer conductivity than copper, which can also drop when the battery is discharged. To put it more precisely, a battery does not become “empty”, but the internal resistance becomes so great through chemical processes that the required current can no longer be drawn.

### Differential internal resistance

If the output voltage is monitored electronically, it can be kept constant quite well if a control system counteracts the deviation and changes the static internal resistance quickly enough. For example, there are inexpensive fixed voltage regulators . In extreme cases, the internal resistance of laboratory power supplies can even reach slightly negative values, which means that the output voltage increases somewhat with increasing load and compensates for the voltage loss due to the ohmic resistance of longer connecting cables to the load. An exaggerated negative resistance can, however, cause undesirable oscillations .

In laboratory power supplies, the internal resistance is current-dependent: up to a certain maximum current, it is very small so that the voltage output hardly changes under load. If this is exceeded, an internal monitoring circuit changes the internal resistance to very high values. Laboratory power supply units then work as a constant current source, whereby with decreasing external resistance (up to a short circuit) the output voltage becomes smaller and smaller without destroying the power supply unit.

### Dynamic internal resistance

The power demand is seldom constant, especially not with electronic circuits. In computers, the power requirements of individual integrated circuits can change in nanosecond intervals. Because this corresponds to a frequency in the gigahertz range, the inductance of the power supply lines cannot be ignored, even if they are only a few centimeters short. The inductive resistance of the wire increases the internal resistance of the voltage source quite considerably with increasing frequency. As a result, the voltage on the component can fluctuate between 2 V and 10 V, for example, even with changes in current, and can disrupt, possibly even destroy, the IC. A control system does not react quickly enough, so low-inductance capacitors are used directly at the IC connections as an antidote . Since capacitors also have a certain self-inductance and do not filter equally well in the entire frequency range between zero and 5 GHz, electrolytic capacitors and ceramic capacitors with as different dielectrics as possible are usually connected in parallel.

A classic example of what can be achieved by reducing the internal resistance is the electronic flash unit . The small, built-in battery has such a large internal resistance that a maximum of about 0.5 W can be extracted when the power is adjusted. This is why a capacitor is charged with the help of a DC voltage converter , from which a peak power of a few kilowatts can then be obtained because of its considerably lower dynamic internal resistance.

## Determination of the static internal resistance

The source resistance R i cannot be measured with an ohmmeter , it can only be determined indirectly:

For example, one measures the output voltage with no load and then with a known load R a . If, for example, the output voltage is half as high as in no-load operation, then R i = R a (the assembly is called a black box ).

For example, if the starter battery of a car with an open circuit voltage U 0  = 12 V only outputs U k  = 10 V when a 0.5 Ω resistor is connected, the internal voltage drop is 2 V and consequently R i  ≈ 0.1 Ω. The internal resistance can change as a function of the state of charge and is the sum of the resistance of the lead plates, their boundary layers and the electrolyte (acid filling).

If a 1.5 V mono cell only outputs I k  = 10 mA at maximum, i.e. in the event of a short circuit, it has an internal resistance of 150 Ω. Usually, one then says that the battery is empty, which, from an electrical point of view, manifests itself as an increase in internal resistance.

The formulas apply to the internal resistance R i :

${\ displaystyle R _ {\ mathrm {i}} = {\ frac {U_ {0} -U _ {\ mathrm {l}}} {I _ {\ mathrm {l}}}} \ qquad (1)}$ ${\ displaystyle = {\ frac {(U_ {0} -U _ {\ mathrm {l}}) R _ {\ mathrm {l}}} {U _ {\ mathrm {l}}}} \ qquad (2)}$ ${\ displaystyle = {\ frac {U_ {0}} {I _ {\ mathrm {k}}}} \ qquad (3)}$ With

U 0 - open circuit voltage
U l - terminal voltage under load
I l - load current (quotient of terminal voltage and load resistance)
I k - short circuit current

## Practical approach

When working on live parts, the applicable safety regulations must be observed. See low voltage . Furthermore, it must be ensured that the operation of amplifiers without a corresponding terminating resistor can lead to their destruction. It is essential to follow the operating instructions.

In most cases it is not practical to measure the current (especially with increasing frequency ) with sufficient accuracy. The following approach saves a second measuring instrument, since only the voltage is measured. Errors with correct current or voltage measurement can also be avoided. To do this, you need a resistor that must meet the following requirements:

• the resistance value should not deviate extremely from the expected internal resistance in order to keep the measurement error as low as possible.
• the maximum current carrying capacity of the source must not be exceeded.
${\ displaystyle R _ {\ mathrm {mess}} \ geq {\ frac {U_ {0}} {I _ {\ mathrm {max}}}}}$ With

R meas - used load resistance
I max - maximum current of the source
• The prescribed terminating or nominal resistance value must be used for amplifiers.
• Ground resistances should be used with increasing frequencies in order to avoid inductive reactances. As an “alternative” solution, 10 to 20 metal film resistors connected in parallel are also suitable . The value of the individual resistances results from the multiplication of R mess with the number of individual resistances.
• the power loss of the load resistor is calculated from
${\ displaystyle P _ {\ mathrm {mess}} \ geq {\ frac {U _ {\ mathrm {0}} ^ {2}} {R _ {\ mathrm {mess}}}}}$ .

With resistors connected in parallel, the power loss is divided by the number of individual resistors.

First, the exact value of the load resistance R mess is determined. The open circuit voltage U 0 is now measured. The measurement is then repeated when the source ( U l ) is loaded by means of the load resistance. From the values ​​determined in this way, the internal resistance can be calculated using formula 2).

## Effect on parallel connection

In an ideal voltage source , that a voltage source without any internal resistance, can be more consumers each other parallel switch , is that the voltage and hence the current to the recent consumers without changes. Only the total current in the circuit increases. However, since there is an internal resistance in a real voltage source , the increase in the total current leads to a decrease in the voltage at the consumers connected in parallel (because the voltage drop across the internal resistance increases) and thus the individual current of the previous consumers through the additional consumers connected in parallel is considered separately decreases. Despite this decrease in the individual currents, the total current increases with each new consumer with the limit value of and, as a result, the voltage at the consumers connected in parallel with the limit value 0 V decreases. Because of this, the parallel connection of devices within certain limits is possible because although the voltage at each parallel consumer is the same, but this decreases with each new parallel branch and at some point no longer sufficient to provide a consumer with its respective minimum power P supply. ${\ displaystyle {\ tfrac {U} {R _ {\ mathrm {i}}}}}$ ## designation

Often the load, external or input resistance is referred to as and the source, internal or output resistance as , which always leads to misunderstandings because external resistance (load) cannot be the output resistance (source). The designations and are to be avoided because only the external, load or input resistance can be. ${\ displaystyle R _ {\ mathrm {e}}}$ ${\ displaystyle R _ {\ mathrm {a}}}$ ${\ displaystyle R _ {\ mathrm {e}}}$ ${\ displaystyle R _ {\ mathrm {a}}}$ ${\ displaystyle R _ {\ mathrm {a}}}$ There are two ways of looking at things (see right figure):

• as an " interface " for two interconnected devices and
• as a device with input and output.

The external resistance is the load resistance and the output resistance is the source impedance or the internal resistance.

Outputs are also referred to as active , inputs as passive . In special cases, however, both can automatically adapt to the respective level or load impedance.

When an output is short-circuited, a short-circuit current flows which, in simple circuits without current limitation, can be calculated from the open circuit voltage and the output resistance.

## Output resistance values

In general, the maximum power is drawn from a circuit when the external resistance is equal to the output resistance ( power matching ). In communications engineering, this is often the case when it comes to fully utilizing the smallest of outputs, for example from receiving antennas. The same applies in telecommunications and communications technology: The highest power can be transmitted if the output resistance matches the input resistance of the next module. This is the power adjustment that is often common there, with the result that the output voltage is half as large as the open circuit voltage. ${\ displaystyle R _ {\ mathrm {i}} = R _ {\ mathrm {a}}}$ In power engineering , the output resistance of the transformers is kept very small compared to the external resistance (i.e. the equivalent resistance of all connected consumers). The reasons for this are:

• High efficiency
• Voltage constancy
• low thermal load on the source

It is also said that an energy supply network works almost at idle .

An amplifier has an input resistance (load resistance, external resistance or terminating resistance of the source feeding it) on one input side and an output resistance (source resistance or internal resistance of the amplifier output) on the output side.

In hi-fi technology and sound engineering, the output resistance of one device must be smaller than the input resistance of the following device, which is also known as voltage adjustment. Reasons:

• you want to measure or amplify the voltage drop across, so it should be much larger than the voltage drop across. This ensures a good signal-to-noise ratio.${\ displaystyle R _ {\ mathrm {a}}}$ ${\ displaystyle R _ {\ mathrm {i}}}$ • A loudspeaker is attenuated all the better (it then has better transmission properties) if it is fed from a source with a low source impedance.
• With a dynamic microphone, the output resistance is relatively small; in studio technology 150 or 200 .${\ displaystyle \ Omega}$ • In the case of a condenser microphone, the source resistance at the location of the membrane condenser is very high (order of magnitude: Gigaohm), but at the microphone output it is 35 to 150, converted to impedance, in the case of studio microphones  .${\ displaystyle \ Omega}$ • In the case of a battery or a rechargeable battery, the output resistance should be as small as possible so that the energy contained can be used effectively; it increases towards the end of the service life and with increasing discharge. It is often very dependent on the temperature.

In amplification systems according to the IRT - specification . No. 3/5 (mixing consoles) the internal resistance is less than 40 ohms over the entire frequency range to be 15 kHz to 40 Hz. The outputs according to the specification are also symmetrical and floating. ${\ displaystyle R _ {\ mathrm {i}}}$ In contrast, high-voltage sources for laboratory purposes usually have a deliberately high output resistance in order to limit the current to 20 mA.

When connecting several assemblies, the respective internal resistance must be observed.

The internal resistance of loudspeaker power amplifiers is rarely given in the data sheets, but it should be as small as possible compared to the load impedance (2, 4 or 8 Ohm minimum loudspeaker impedance). If the damping factor D F is known, it can be determined by: ${\ displaystyle R _ {\ mathrm {i}}}$ ${\ displaystyle R _ {\ mathrm {i}} = {\ frac {R _ {\ mathrm {a}}} {D _ {\ mathrm {F}}}}}$ The attenuation factor is particularly high for the loudspeaker when the power amplifier has a low source impedance. Common transistor amplifiers have source impedances of <0.1 Ohm. In order not to increase the output resistance unnecessarily through supply lines, the cables (depending on their length and load impedance) must have a sufficient cross-section.

At each interface , the output resistance of the source and the input resistance of the load form a matching damping .

## The impedances and their different names

R i R a
Internal resistance External resistance