Circuit Elements: Active, Passive, Independent, and Dependent Sources with Sign Convention

Active circuit elements
- Definition: sources that deliver power (provide energy) to a circuit
- Examples mentioned: generators, batteries, operational amplifiers (op-amps to be discussed later)
- In class focus: start with sources, then later discuss op-amps explicitly
Passive circuit elements
- Definition: elements that absorb energy from a circuit
- Examples shown: resistor, in series with an inductor and a capacitor (series R-L-C)
- In early weeks: exclusive focus on resistors; after the first exam, capacitors and inductors are introduced when time-variant analysis is covered

Current source
- Produces a specified positive current in a given direction (arrow direction shown in drawings)
- Whatever circuit is connected across its terminals will receive that current
- Ideal current source characteristics: infinite internal resistance; will force a fixed current regardless of the circuit connected
Voltage source (two representations)
- General description: voltage across two terminals is fixed, with a defined positive and negative terminal
- Battery symbol representation: longer line = positive terminal, shorter line = negative terminal
- Plus/minus signs are added for clarity
- In circuit diagrams (e.g., Multisim): the standard symbol shows across two terminals a fixed voltage regardless of load
- If a circuit is connected across these two points, the voltage between them remains the stated voltage $V = V_s$

Independent sources
- Value is fixed and does not depend on other circuit parameters
- Depicted as circles in circuit diagrams
Dependent (controlled) sources
- Output depends on another circuit parameter (e.g., a current or voltage elsewhere in the circuit)
- Represented by diamonds in diagrams
- If you see a diamond with a plus/minus, it is a dependent voltage source; if you see an arrow, it is a dependent current source
- Types (four typical configurations):
- Voltage-controlled voltage source (VCVS)
- Current-controlled voltage source (CCVS)
- Voltage-controlled current source (VCCS)
- Current-controlled current source (CCCS)
- These are ideal dependent sources unless otherwise stated

Diagrammatic example: a dependent voltage source shown as a diamond with a plus/minus sign
Value example: the dependent voltage source has a value $V_{dep} = 10 imes I$ where $I$ is the current through element C
- This means the voltage output of the dependent source changes in response to the current through another element (element C)
- The current through element C may depend on the resistance of element C or other circuit parameters
- This illustrates how a dependent source’s output is controlled by another part of the circuit

Ideal voltage source
- No internal resistance: $R_{int} = 0$
- Practically, it can produce any current necessary to keep the terminal voltage at the stated value $V_s$ , regardless of the load
- Example: an ideal 5 V source maintains 5 V even if a wire is shorted across its terminals (in theory)
Ideal current source
- Infinite internal resistance: it enforces a fixed current $I_s$ regardless of the voltage across it
- The resulting terminal voltage can be any value necessary to maintain that current
Practical caveats
- In reality, voltage sources have an upper limit on current they can supply
- Similarly, current sources have an upper limit on the voltage they can develop
- These limits will be explored in labs and simulations
Practical note for problems
- When not stated otherwise, you can assume ideal sources for circuit analysis problems

Passive sign convention
- If current enters the element at the terminal labeled positive, the power is considered positive if the element is absorbing power
- Power definition under this convention: $P = V imes I$ where $V$ is the voltage across the element with the positive terminal at the point where the current enters
- Implications
- If the element is absorbing energy (e.g., a resistor), $P > 0$ (positive power)
- If the element is delivering energy to the rest of the circuit (e.g., a battery or generator), the current leaves the terminal with the higher potential, yielding $P < 0$
Example interpretation
- If asked how much power is provided by a source, and you apply the passive sign convention, you would report a negative power value for a source delivering power

Power with passive sign convention: $P = V I$
Ideal voltage source: terminal voltage fixed, current adjustable, V = Vs, ightarrow I ext{ determined by load}, R{int} = 0
Ideal current source: current fixed, voltage adjustable, I = Is, ightarrow V ext{ determined by circuit}, R{int} =
fty
Dependent source output depends on another circuit parameter (e.g., current or voltage elsewhere)
Dependent source symbol shapes: independent sources (circle), dependent sources (diamond)
Dependency types (representations): VCVS, CCCS, VCCS, CCVS
Example relation for a dependent voltage source: $V_{dep} = 10 imes I$ (where $I$ is the current through a specified element, e.g., element C)

You will encounter both independent and dependent sources in circuits; be able to distinguish by symbol shape (circle vs diamond) and by the presence of control relationships (dependent sources)
Remember the passive sign convention to correctly determine whether a element is absorbing or delivering power
When solving problems, treat sources as ideal unless the problem explicitly states non-ideal characteristics; acknowledge non-ideal behavior when noted
Real-world sources have limits; consider these when reasoning about short circuits or extreme load conditions
After initial topics (resistors) focus will shift to capacitors and inductors for time-domain and time-variant circuit analysis