The Importance of Reference Polarities in a Circuit
Passive Sign Convention
The Importance of Reference Polarities in a Circuit:
Passive Sign Convention
Introduction
When creating an electrical circuit, the fundamental goal is to apply voltages to the circuit such that the current is directed to perform some useful task. In order to do this, it is absolutely necessary to keep track of the voltage polarity relative to the current direction1 . This requires that we understand the rigorous definition of the sign conventions involved. The sign convention used by electrical engineers is the passive sign convention—so called since it applies to passive circuit elements2 . This section presents the sign convention used in electrical circuit analysis—it is simple, but it must be followed rigorously or disaster will result!
A two-terminal electrical circuit element is shown in Fig. 1. There is some current, I , flowing through the element and some voltage difference, V, across its terminals.
On Fig. 1, the assumed direction for current is shown by the arrow, and the assumed polarity of the voltage is indicated by the “+” and “-” signs. Please remember that the current direction and voltage polarity shown on Fig. 1 do not specify the actual current direction and voltage polarity—they only provide references which allow us to interpret the actual voltage and current. This is an extremely important point; if you are at all uncomfortable with this concept, you may want to re-read the voltage and current sections provided through the links to the right.
Individually, the assumed voltage polarity and current direction shown on Fig.1 are not important, but the voltage polarity relative to current direction is important. We need to define voltage polarity and current direction so that they obey the passive sign convention:
- Voltage polarities and current directions should be defined such that positive current enters the node at which the positive voltage polarity is defined. This sign convention is consistent with the definitions of Fig. 1.
The passive sign convention is actually extremely simple to employ. You can choose either the reference current direction or the voltage polarity arbitrarily. However, once you have chosen one of these, the other must be chosen such that the passive sign convention is obeyed.
It is important to keep in mind that the currents and voltages we are specifying here are not the actual, physical values. Current may actually enter the negative voltage terminal, but this information will be provided as a negative sign on either the voltage or current values—the reference directions must be set according to the passive sign convention.
The reason for using the passive sign convention is because we describe circuit elements according to the voltage-current relationships at their terminals. These relationships invariably assume that the passive sign convention is being obeyed. This is only true for so-called passive circuit elements - these elements do not supply power to the circuit. Voltage and current sources are not passive elements, and it is not necessary to follow the passive sign convention for them3 .
Examples:
- The passive sign convention is satisfied for either of the two voltage-current definitions shown below—in both cases, positive current enters the positive voltage node.
- The passive sign convention is not satisfied for either of the two voltage current definitions shown below—positive current is assumed to enter the negative voltage node in both cases.
Important Points:
- For passive circuit elements, choose reference voltage polarities and current directions according to the passive sign convention:
- The reference current direction must enter the positive reference voltage node.
- Either the reference voltage polarity or the reference current direction
can be chosen arbitrarily. After this choice is made, though, it dictates the
choice of the other parameter. Therefore:
- Choice of a positive direction for current dictates the choice of positive voltage polarity.
- Choice of a positive voltage polarity dictates the choice of positive current direction.
It is tempting to try to assign reference voltage polarities and current directions so that the actual currents and voltages in the circuit are always positive. At best, this is a waste of time and at worst, it is impossible. Just arbitrarily choose your reference voltage polarity or current direction for each circuit element, assign the other parameter according to the passive sign convention, and get on with your life!
It is only necessary to obey the passive sign convention for elements which do not provide power to the circuit—you don't need to follow the passive sign convention for voltage and current sources.
Test Your Knowledge!
Either the reference voltage polarity or the reference current direction is provided for the circuit elements below. Provide the appropriate sign convention for the missing parameters.
A circuit schematic is shown. Which of the options below provide a valid choice of voltage and currents for the elements?
- Possible choices:
A circuit schematic is shown. Which of the four options below provide a valid choice of voltage and currents for the elements?
- Possible choices:
Selected Answers
-
All four choices are valid. In any element, current enters the positive voltage terminal.
(a) , (c) , and (d) are valid. In (b), the voltage and current for element 1 do not agree with the passive sign convention.
- 1 We'll see later that this relationship defines which circuit elements absorb power and which elements generate power. If we don't keep the relationship straight, we fail at our primary task—keeping track of how energy is being transferred!
- 2 Passive elements don't add energy to our circuit. Voltage and current sources add energy to a circuit, and are not passive elements. We don't need to follow the passive sign convention for sources.
- 3 The behavior of voltage and current sources is not described by voltage-current relations at their terminals. Remember that we know nothing about the current through a voltage source or the voltage across a current source!
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