Formula Reference

Relates voltage, current and resistance in a DC circuit.

Power dissipated or delivered in a DC circuit.

Output voltage of a resistive voltage divider.

Total resistance of resistors connected in series.

Total resistance of resistors connected in parallel.

Energy stored in a capacitor.

Energy stored in an inductor.

Opposition of a capacitor to AC current.

Opposition of an inductor to AC current.

Total impedance of a series RLC circuit.

Real (active) power in an AC circuit.

Cutoff frequency of a first-order RC low-pass or high-pass filter.

Cutoff frequency of a first-order RL filter.

Resonant frequency of an LC or RLC circuit.

Quality factor — sharpness of resonance.

Closed-loop voltage gain of an inverting op-amp configuration.

Closed-loop voltage gain of a non-inverting op-amp.

Maximum rate of change of output voltage.

DC current gain (hFE) of a BJT transistor.

Emitter current equals collector plus base current.

Drain current of an NMOS in saturation region.

Average propagation delay of a logic gate.

Maximum clock frequency limited by propagation delay.

High and low noise margins of a logic gate.

Total real power in a balanced three-phase system.

Ratio of real power to apparent power.

Relationship between turns ratio, voltage and current.

Voltage gain expressed in decibels.

Power gain expressed in decibels.

Minimum sampling frequency to avoid aliasing.

Time for RC circuit to charge to 63.2% of final voltage.

Depth at which current density falls to 1/e of surface value.

Wavelength of an electromagnetic wave in free space.

Minimum trace width for a given current — simplified IPC-2221 external layer.

DC resistance of a PCB trace.

Sum of currents entering a node equals sum of currents leaving.

Thévenin equivalent voltage equals the open-circuit voltage at terminals.

Maximum power delivered to load when RL = Rth.

Current through a parallel branch.

Convert star (Y) resistor network to delta (Δ).

Reactive power stored and released by inductors and capacitors.

Total power supplied to an AC circuit.

Capacitor needed to correct lagging power factor.

RMS value of a sinusoidal voltage waveform.

Angular frequency of a sinusoidal signal.

Voltage response of RC circuit during charging or discharging.

Time constant of an RL circuit.

Damping ratio determines RLC transient response type.

Actual oscillation frequency of underdamped RLC circuit.

Impedance of inductor in Laplace s-domain.

Impedance of capacitor in Laplace s-domain.

Fundamental frequency and angular frequency of a periodic signal.

Line voltage in a balanced star (Y) connected system.

Line current in a balanced delta (Δ) connected system.

Total reactive power in a balanced three-phase system.

Total apparent power in a balanced three-phase system.

Mutual inductance between two magnetically coupled coils.

Convert transfer function magnitude to decibels for Bode plot.

DC gain of a transfer function found by setting s=0.

Output of a PID controller based on error signal.

Time for response to settle within 2% of final value.

Maximum percentage overshoot in underdamped step response.

How much gain can increase before system becomes unstable.

Time for response to rise from 10% to 90% of final value.

Speed of a DC motor in terms of supply voltage and back EMF.

Electromagnetic torque developed by a DC motor.

Back EMF generated in armature of DC motor.

Generated EMF in a DC generator.

Efficiency of a DC motor or generator.

Efficiency of a transformer accounting for core and copper losses.

Percentage voltage regulation of a transformer.

Copper (I²R) loss in transformer windings.

Synchronous speed of an AC induction motor.

Slip of an induction motor — difference between sync and rotor speed.

Frequency of currents in the rotor of an induction motor.

Mechanical power output from induction motor.

Average DC output voltage of a half-wave rectifier.

Average DC output voltage of a full-wave rectifier.

Measure of AC ripple in DC output of a rectifier.

Duty cycle of a switching converter or PWM signal.

Output voltage of an ideal buck (step-down) DC-DC converter.

Output voltage of an ideal boost (step-up) DC-DC converter.

Output voltage of an ideal buck-boost DC-DC converter (inverted).

Current through a diode using the Shockley diode equation.

Thermal voltage at a given temperature (≈26mV at 300K).

Common-base current gain of a BJT transistor.

Small-signal transconductance of a BJT at operating point.

Balance condition for a Wheatstone bridge circuit.

Sensitivity of a voltmeter in ohms per volt.

Amplitude modulation index ratio of message to carrier amplitude.

Frequency modulation index ratio of frequency deviation to message frequency.

Maximum data rate of a noisy channel (Shannon-Hartley theorem).

Signal-to-noise ratio expressed in decibels.

Battery capacity in ampere-hours.

Total energy stored in a battery.

Physical length of a half-wave dipole antenna.

Signal attenuation in free space between transmitter and receiver.

Norton equivalent current equals short-circuit current at terminals.

Total capacitance of capacitors in series.

Total capacitance of capacitors in parallel.

Total inductance of inductors in series.

Total inductance of inductors in parallel.

Electric charge transferred by current over time.

Electrical conductance is the reciprocal of resistance.

Resistance of a conductor based on material and dimensions.

Change in resistance due to temperature change.

Relationship between period and frequency of a signal.

Magnitude of complex impedance.

Phase angle between voltage and current in AC circuit.

Bandwidth of a bandpass filter.

Resonant frequency of an LC filter circuit.

At cutoff frequency, output is 70.7% of maximum (−3dB).

Output of an inverting summing op-amp amplifier.

Output of an op-amp differentiator circuit.

Gain of op-amp integrator at a given frequency.

Gain-bandwidth product is constant for an op-amp.

Convert binary number to decimal.

Maximum number of gates a logic gate output can drive.

Dynamic power dissipation in CMOS logic gates.

Steady state error for step input with position constant Kp.

Phase margin indicates stability — positive PM means stable.

Natural frequency of a second order system.

Power lost in transmission line resistance.

Per unit system normalizes power system quantities.

Base impedance for per unit calculations in power systems.

Electrical input power to a DC motor armature.

Mechanical power developed in DC motor armature.

Field current in a shunt DC machine.

Efficiency of an induction motor.

Synchronous motors run exactly at synchronous speed.

Power lost in rotor resistance of induction motor.

Average output voltage of half-wave SCR rectifier with firing angle α.

RMS output voltage of single phase PWM inverter.

Power lost during switching transitions in power converters.

Magnetic flux through a surface.

Induced EMF is proportional to rate of change of magnetic flux.

Magnetomotive force in a magnetic circuit.

Opposition to magnetic flux in a magnetic circuit.

Magnetic flux density inside a solenoid.

Power output of a solar panel.

Power extracted from wind by a turbine.

Fill factor measures quality of a solar cell.

Current ratio is inverse of turns ratio in ideal transformer.

Apparent power rating of a transformer.

Impedance seen at primary when load is connected to secondary.

Maximum efficiency occurs when core loss equals copper loss.

Energy efficiency of transformer over 24 hours.

Voltage ratio of an auto-transformer.

Percentage short circuit voltage of transformer.

Bandwidth of an amplitude modulated signal.

Bandwidth of FM signal using Carson's rule.

Total power of an AM signal including sidebands.

Bit rate based on sampling frequency and modulation order.

Received power in a wireless link.

Degradation of SNR through a component.

Wavelength of electromagnetic wave at given frequency.

Maximum current a PCB via can carry.

Characteristic impedance of a PCB microstrip trace.

3W rule to minimize crosstalk between PCB traces.

Decoupling capacitor needed for transient current demand.

Junction temperature of component on PCB.

Voltage drop across a PCB trace carrying current.

Output length of convolution of two discrete signals.

Total energy of a discrete time signal.

Average power of a periodic signal.

Time delay property of Z-transform.

Frequency resolution of a Discrete Fourier Transform.

Apparent frequency when signal is undersampled.

Sum of all voltages around any closed loop equals zero.

Heat generated by current flowing through resistance.

Electric field between two parallel plates.

Quality factor of a series RLC circuit at resonance.

Quality factor of a parallel RLC circuit at resonance.

Series resistor for zener diode voltage regulator.

Drain current of NMOS in triode (linear) region.

Base voltage in voltage divider bias circuit.

Short circuit current in a power system.

Percentage voltage regulation of a transmission line.

Closed loop transfer function with feedback.

Time for response to reach 50% of final value.

Force between two point charges.

Total charge enclosed equals permittivity times electric flux.

Force on a charged particle in electric and magnetic fields.

Capacitance of a parallel plate capacitor.

Bandwidth is difference between highest and lowest frequencies.

Power gain of an amplifier expressed in decibels.

Maximum power a resistor can safely dissipate.

Average velocity of electrons in a conductor.

RMS value of a triangular waveform.

Ratio of peak value to RMS value of a waveform.

Ratio of RMS value to average value of a waveform.

Current during capacitor charging in an RC circuit.

Passband gain of a Sallen-Key second order active filter.

Common Mode Rejection Ratio of an op-amp.

Drain current of a JFET in saturation region.

Boolean expressions for half adder circuit.

No-load current of a transformer combining core loss and magnetizing components.

Reactive power provided by a Static VAR Compensator.

Gain value at a specific point on the root locus.

Speed of light in vacuum — exact defined value.

Charge of a single electron or proton.

Electric constant — permittivity of free space.

Magnetic constant — permeability of free space.

Free space impedance for electromagnetic waves.

Fundamental constant relating energy and frequency.

Relates energy at the particle level to temperature.

Number of particles in one mole of substance.

Rest mass of an electron.

Rest mass of a proton.

Thermal voltage at room temperature, used in diode equations.

Energy gap of silicon at room temperature.

Intrinsic carrier concentration of silicon at room temperature.

Electrical resistivity of copper at room temperature.

Electrical resistivity of aluminum at room temperature.

Electrical resistivity of silver — best conductor.

Standard 1oz copper thickness used in PCB manufacturing.

Dimensionless constant characterizing electromagnetic interaction strength.

Most probable distance between proton and electron in hydrogen atom.

Energy gap of Gallium Arsenide — used in high frequency devices.