AMERC: Electronic Principles formula sheet Ohms law: Ohms law π = πΌπ (V) Voltage divider πππ’π‘ = πππ × π Resistors: In series In parallel π π‘ππ‘ππ = π 1 + π 2 + π π … (β¦) −1 −1 −1 −1 π π‘ππ‘ππ = (π 1 + π 2 + π π … ) π 2 1 +π 2 (V) (β¦) KCL: For two DC loops, the currents πΌ1 and πΌ2 in each branch can be generalised as a set of simultaneous equations in the form: π1 = πΌ1 (π 1 + π 2 ) + π 2 πΌ2 π2 = π 2 πΌ1 + πΌ2 (π 2 + π 3 ) Where: π 1 , π 2 , π 3 are the resistance values on the diagram and π1 , π2 are the voltages of the two DC sources. Power: In general π = πΌπ, π = πΌ 2 π , π = π2 π (W) Capacitors: π π Capacitance πΆ= In series In parallel πΆπ‘ππ‘ππ = (πΆ1−1 + πΆ2−1 + πΆπ−1 … )−1 πΆπ‘ππ‘ππ = πΆ1 + πΆ2 + πΆπ … Energy stored πΈ= Charge stored π = πΆπ (F) 1 πΆπ 2 2 (F) (F) (J) (C) ππ‘ππ‘ππ πΆ Voltage across a capacitor ππ = RC, RL Circuits: Time constant (RC) π = π πΆ (V) (s) πΏ π Time constant (RL) π= RC charging equation ππ = π0 (1 − π)−π πΆ , πΌπ = πΌ0 π −π πΆ RC discharging equation ππ = π0 π −π πΆ , πΌπ = πΌ0 (1 − π)−π πΆ RL charging equation ππΏ = π0 π − πΏ , πΌπΏ = πΌ0 (1 − π)− πΏ RL discharging equation ππΏ = −π0 (1 − π)− πΏ , πΌπΏ = πΌ0 π − πΏ (s) π‘ π‘ π‘ π‘ π π‘ π π‘ π π‘ π π‘ Op-Amps: πππ’π‘ ) πππ Gain in general π΄π£ = ( Non-Inverting πππ’π‘ = πππ × (1 + π π) (V) Inverting Summing π π π 2 πππ’π‘ = πππ × −(π ) (V) 2 π π πππ’π‘ = −( π 1 × π1 + π π π 2 × π2 + π π π π × ππ … ) (V) AC: 2π , (s) π π 1 ,π = π 2π Time period π= Frequency π= Equation of an AC waveform ππ‘ = πππ sin(ππ‘ + π), πΌπ‘ = πΌππ sin(ππ‘ + π) RMS ππππ = Capacitive reactance ππΆ = Inductive reactance ππΏ = 2πππΏ Impedance Phase angle Current π= π = 2ππ (Hz) πππ (V) √2 1 2πππΆ √π 2 (β¦) (β¦) + (ππΆ − ππΏ )2 (β¦) NB. ππΆ > ππΏ π −π π = tan−1 ( πΆ π πΏ ) π πΌ = π (A) Resonance ππΆ = ππΏ Resonant Frequency π= 1 2π√πΏπΆ Q-factor π= 1 π (Hz) πΏ × √πΆ Transformers: Voltage-turns Relationship Current relationship Matching ππ ππ = ππ ππ ππ πΌπ = ππ πΌπ ππ ππ π = ( π )2 ππ dB’s π As a function of Power 10log ( πππ’π‘ ) As a function of voltage/current π πΌ 20 log ( πππ’π‘ ) , 20 log ( πΌππ’π‘ ) ππ ππ ππ Power Supplies: Ripple voltage πππππππ = πΌπΏ π πΆ πΌπΏ = Load current, π = time period Wien bridge oscillators: 1 2ππ πΆ Frequency π= Minimum gain π΄π£ > 3 (Hz) Boolean Logic: AND π = π΄ β π΅ OR π =π΄+π΅ NOT π = π΄Μ NAND π = Μ Μ Μ Μ Μ Μ π΄βπ΅ XOR π = π΄β¨π΅ Μ Μ Μ Μ Μ Μ Μ XNOR π = π΄β¨π΅ Diodes & transistors Silicon diode volt drop NPN transistor (When saturated) PNP transistor (When saturated) We assume that ≈ 0.7 (V) ππ = ππ − πππ (V) ππ = ππ + πππ (V) πΌπ = πΌπ NB. πππ is typically 0.7 V NB. πππ is typically 0.7 V