02 · Introductory

Receiver and generator conventions

The relative orientation of voltage and current references determines the sign of power.

70-95 minIntroductory

In this lesson

Recognize receiver/passive convention.
Recognize generator convention.
Use P=VI with the chosen references.
Separate component role from sign convention.

Starting question

How can the same pair of numbers V and I describe a device absorbing energy in one reference convention and delivering energy in another?

The answer is not that power changed physically. The algebraic meaning of VI depends on how the current reference is oriented relative to the positive voltage terminal.

02.1Receiver/passive convention

Figure 2.1 — Receiver (passive) conventionThe positive current reference enters the positive terminal. With AoN's voltage arrow running from − to +, the V and I arrows point in opposite directions.

Figure 2.2 — Generator conventionThe positive current reference leaves the positive terminal. With the same voltage reference, the V and I arrows point in the same direction.

In receiver convention, positive current enters the terminal defined positive by the voltage reference. With AoN's voltage arrow from − to +, the current and voltage arrows point in opposite directions.

P_absorbed = V I

Pabsorbed>0: the element absorbs energy.
Pabsorbed<0: the element is actually delivering energy.

02.2Generator convention

In generator convention, the positive current reference leaves the positive voltage terminal. With AoN arrows, voltage and current arrows now have the same orientation.

If we still define P_absorbed as positive for absorption, then

P_absorbed = −V I

Equivalently, VI can be interpreted as delivered power under the generator convention. The important point is to state which quantity is being called positive.

02.3Same physical operating point, different algebraic variables

Take a two-terminal device with 12 V between its terminals and a physical current of 0.5 A entering the positive terminal. Under receiver convention, V=+12 V and I=+0.5 A, so

P_absorbed=+6 W

If we redefine the current arrow in the opposite direction, the new current variable is −0.5 A. The physical device has not changed; only the coordinate used to describe current has.

02.4A battery is not permanently a “generator”

A rechargeable battery can deliver energy while discharging and absorb energy while charging. Calling the component a “source” does not remove the need to inspect the signed voltage/current variables.

Receiver convention: V=12 V and I=−0.5 A. What happens?

Pabsorbed=−6 W, so the device delivers 6 W.

02.5Why both conventions exist

Receiver convention is convenient when the natural question is “how much power does this element absorb?” Generator convention is convenient when the natural question is “how much power does this source deliver?” Neither changes the physics.

AoN will normally use receiver convention unless another choice makes a derivation substantially clearer. When a different convention is used, it must be stated explicitly.

02.6Practice for mastery

Receiver convention: V=5 V, I=40 mA. Absorbed power?
Receiver convention: V=5 V, I=−40 mA. Physical interpretation?
Under generator convention, V=10 V and the positive current variable is 0.3 A. What is Pabsorbed?
Explain why “source symbol ⇒ negative power” is not a valid rule.

Solutions

1. +200 mW absorbed.

2. −200 mW absorbed, i.e. 200 mW delivered.

3. Pabsorbed=−3 W.

4. Energy flow depends on operating state and references; a source-like device can absorb energy.