Types of Circuit Elements

Passive Elements

• Dissipate power from the circuit and obey passive sign convention
• Types:
  • Resistors (R)
  • Inductors (L)
  • Capacitors (C)
  • Diodes

Active Elements

• Supply power to the circuit and obey active sign convention
• Types:
  • Voltage sources
  • Current sources
  • Controlled sources
  • Op-amps

Properties of Linear Elements

• Superposition: Output is the sum of individual inputs

• Homogeneity/Scaling: If input is scaled, output scales proportionally

• Combining both properties:

Ohm’s Law

• The potential difference across a resistor is proportional to the current, with a constant of proportionality (slope) being resistance

• $V$ is dependent upon the direction of $i$

Resistors and Resistance

Resistance

• The physical property of an element or device that impedes current flow

Example

Linear Resistors

• Since resistors are linear, $V$ will be a function of $i$ and $R$ will be independent of both $V$ and $i$
  • When two currents $i_1$ and $i_2$ flow through a resistor with resistance $R$ with corresponding voltages $V_1 = i_1R$ and $V_2 = i_2R$, the total voltage would be:

Power Dissipated by a Resistor

• Substituting Ohm’s Law into the power equation:

• Also expressed as:

Independent Sources

• Independent sources are ideal
  • This means they supply a voltage/current regardless of the current drawn or the potential difference across that source
  • In the real world, this is not the case, however

Voltage Source

• Supplies a potential $V(t)$
• The resulting current is a result of the remainder of the circuit
• We usually draw voltage sources to obey the active sign convention, even though the image below obeys passive sign convention

Current Source

• Supplies a current $i(t)$
• The resulting voltage is a result of the remainder of the circuit
• In the real world, this is accomplished by adjusting the voltage to provide the desired current
• We usually draw current sources to obey the active sign convention, even though the image below obeys passive sign convention

Measuring Devices

• Measures current or voltage when models can’t be established
• Red lead goes to (+) terminal, black lead to (-)
  • Otherwise, device will read negative values

Ammeter

• Measures current in A
• Wired in series
• Assume resistance is zero
  • This creates a short circuit; current flows through the device but no potential difference exists

Voltmeter

• Measures potential difference in V
• Wired in parallel
• Assume resistance is infinite
  • This creates an open circuit; no current exists but there is still a potential difference

Dependent Sources

• Used to model transistors and amplifiers
• $b=g=d=r \equiv k$ is the gain of the system

• Current-controlled sources are short circuits
  • This is because current sources don’t restrict current
• Voltage-controlled sources are open circuits
  • This is because voltage sources shouldn’t have voltages when control is removed

Examples

Transducers

• Convert physical quantities to electrical signals

Types

• Potentiometer: Converts rotational position to resistance with $a = \frac{\theta}{360^\circ}$
  • Two branches, one with $R = aR_p$ and the other with $R = (1-a)R_p$
• Temperature Sensor: Converts temperature to current, $i = kT$, where $k = 1 \frac{\mu A}{^\circ K}$

Switches

• Single-Pole Single-Throw is like a light switch and can be used to prevent momentary connection of old and new circuit paths (break before make)
• Single-Pole Double-Throw switches between two branches without ever seeing an open circuit (make before break)

Examples

References

• Course slides, chapter 2: Circuit Elements