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GCSE, AS and A Level	AS and A Level	A Level
systems subsystems inputs (sensing) light temperature magnetic field pressure moisture sound rotation processes individual logic gates latch time delay comparator outputs lamp buzzer solenoid LED actuator servo motor loudspeaker seven-segment display transducer drivers	systems subsystems inputs processes outputs feedback system diagrams outputs lamp buzzer solenoid LED actuator servo motor loudspeaker seven-segment display solenoid relay transducer drivers	systems subsystems inputs processes outputs feedback system diagrams outputs lamp buzzer solenoid LED actuator servo motor loudspeaker seven-segment display solenoid relay transducer drivers
GCSE, AS and A Level	AS and A Level	A Level
circuit symbols measure and calculate voltage current resistance energy power multimeters timing equipment logic probes oscilloscopes rules current voltage series parallel current-voltage characteristics V = IR P = IV P = I2R E = Pt P = V2/R	circuit symbols measure and calculate voltage / potential difference current resistance energy power = rate of doing work multimeters timing equipment logic probes oscilloscopes rules current voltage series parallel current-voltage characteristics V = IR P = IV P = I2R E = Pt P = V2/R RMS VRMS = Vo / √2 IRMS = Io / √2 AC Power and RMS P = IV P = I2R V2 / R	circuit symbols measure and calculate voltage / potential difference current resistance energy power = rate of doing work multimeters timing equipment logic probes oscilloscopes rules current voltage series parallel current-voltage characteristics V = IR P = IV P = I2R E = Pt P = V2/R RMS VRMS = Vo / √2 IRMS = Io / √2 AC Power and RMS P = IV P = I2R V2 / R
GCSE, AS and A Level	AS and A Level	A Level
resistors series R = R1 + R2 parallel R = R1 R2 / (R1 + R2) E24 colour codes tolerances power ratings voltage dividers VOUT = VIN R2 / (R1 + R2) sensing circuits switches photosensitive devices ntc thermistors pressure moisture sound switches pull-up or pull-down logic levels potentiometers pulse generators for timing clock pulses	resistors defined R = V / I V = I R I = V / R series R = R1 + R2 + ... parallel RT = 1 / ( 1 / R1 + 1 / R2 + ... ) R = R1 R2 / (R1 + R2) E24 colour codes tolerances power ratings voltage dividers VOUT = VIN R2 / (R1 + R2) sensing circuits switches photosensitive devices ntc thermistors pressure moisture sound characteristic curves switches pull-up or pull-down logic levels potentiometers pulse generators for timing clock pulses Kirchoff current voltage Thevenin	resistors defined R = V / I V = I R I = V / R series R = R1 + R2 + ... parallel RT = 1 / ( 1 / R1 + 1 / R2 + ... ) R = R1 R2 / (R1 + R2) E24 colour codes tolerances power ratings voltage dividers VOUT = VIN R2 / (R1 + R2) sensing circuits switches photosensitive devices ntc thermistors pressure moisture sound characteristic curves switches pull-up or pull-down logic levels potentiometers pulse generators for timing clock pulses Kirchoff current voltage Thevenin
GCSE, AS and A Level	AS and A Level	A Level
semiconductor diode I-V characteristics protection half-wave rectifier LED calculate series resistor Zener voltage regulation semiconductor switches npn transistor IC = hFE IB up to saturation VIN < 0.7 V transistor is off VBE = VIN VCE = supply voltage VIN = 0.7 V transistor is on VBE = 0.7 V VCE = 0 V n-channel MOSFET ID = gM (VGS - 3) comparator IC interface to outputs	semiconductors n-type p-type p-n junction silicon diode bipolar transistor (npn) IC = hFE IB VIN < 0.7 V transistor is off VBE = VIN VCE = supply voltage VIN = 0.7 V transistor is on VBE = 0.7 V VCE = 0 V MOSFET (n-channel) gM is the ID-VGS graph gradient ID = gM ( VGS - 3 ) P = ID2 RDSon LED Zener diode device characteristic graphs calculations	semiconductors n-type p-type p-n junction silicon diode bipolar transistor (npn) IC = hFE IB VIN < 0.7 V transistor is off VBE = VIN VCE = supply voltage VIN = 0.7 V transistor is on VBE = 0.7 V VCE = 0 V MOSFET (n-channel) gM is the ID-VGS graph gradient ID = gM ( VGS - 3 ) P = ID2 RDSon LED Zener diode device characteristic graphs calculations conduction n-type p-type electrons holes p-n junction forward bias reverse bias LED series resistor photodiode n-channel MOSFET bias, channel (pinching) Zener diode circuit calculations sketching characteristic graphs calculations
GCSE, AS and A Level	AS and A Level	A Level
logic, combinational two-states pull-up and pull-down gates, up to two inputs NOT AND OR NAND NOR truth tables Boolean expressions algebra circuit simplification NAND gate redundancy identities (A.B) = A + B (A + B) = A . B	logic, combinational two-states pull-up and pull-down sourcing sinking gates, up to three inputs NOT AND OR NAND NOR XOR XNOR truth tables Boolean expressions algebra circuit simplification NAND gate redundancy identities (A.B) = A + B (A + B) = A . B de Morgan A . 1 = A A . 0 = 0 A . A = A A . A = 0 A + 1 = 1 A + 0 = A A + A = A A + A = 1 A + A . B = A + B A . B + A = A . (B + 1) = A Karnaugh maps multiplexer	logic, combinational two-states pull-up and pull-down sourcing sinking gates, up to three inputs NOT AND OR NAND NOR XOR XNOR truth tables Boolean expressions algebra circuit simplification NAND gate redundancy identities (A.B) = A + B (A + B) = A . B de Morgan A . 1 = A A . 0 = 0 A . A = A A . A = 0 A + 1 = 1 A + 0 = A A + A = A A + A = 1 A + A . B = A + B A . B + A = A . (B + 1) = A Karnaugh maps multiplexer
GCSE, AS and A Level	AS and A Level	A Level
logic, sequential latches BCD counter decade counter timing diagrams number systems decimal binary binary-coded decimal (BCD) counter timing diagrams conversions D type flip-flop (4013) rising edge timing diagrams data transfer latch up counter 1-bit 2-bit timing diagrams 7-seg' display (common cathode) single 4-bit BCD counter decoder/driver 7-segment display convert number to 7-segment truth table counter reset at given value timing diagram sequence logic 4017 decade counter sequencer timing diagram	logic, sequential latches BCD counter decade counter timing diagrams number systems hexadecimal decimal binary binary-coded decimal (BCD) counter timing diagrams conversions D type flip-flop (4013) D, Ck, Q, Q, R, S rising edge timing diagrams data transfer latch up counter 1 to 4 bit timing diagrams 2 digit BCD counter synchronous counter 7-seg' display (common cathode) single 4-bit BCD counter decoder/driver 7-segment display convert number to 7-segment truth table counter reset at given value timing diagram sequence logic 4017 decade counter sequencer timing diagram NAND latch RS bi-stable flip flop propagation delay transition gates frequency divider asynchronous counter 4 bit counter logic controller 2 digit decimal counter & reset	logic, sequential latches BCD counter decade counter timing diagrams number systems hexadecimal decimal binary binary-coded decimal (BCD) counter timing diagrams conversions D type flip-flop (4013) D, Ck, Q, Q, R, S rising edge timing diagrams data transfer latch up counter 1 to 4 bit timing diagrams 2 digit BCD counter synchronous counter 7-seg' display (common cathode) single 4-bit BCD counter decoder/driver 7-segment display convert number to 7-segment truth table counter reset at given value timing diagram sequence logic 4017 decade counter sequencer timing diagram NAND latch RS bi-stable flip flop propagation delay transition gates frequency divider asynchronous counter 4 bit counter logic controller 2 digit decimal counter & reset shift register PISO SIPO synchronous counter sequence generators D-type flip-flops synchronous counters state diagrams stuck states unused states Boolean simplification
GCSE, AS and A Level	AS and A Level	A Level
op-amps gain calculations G = VOUT / VIN inverting G = - RF / R1 non-inverting G = 1 + RF / R1 summing VOUT = - RF ( V1 / R1 + V2 / R2 + ... ) summing mixer circuit gain-frequency graph measure bandwidth from graph gain bandwidth compromise I/O voltage-time graphs normal clipping distortion typical amplifier signal source preamplifier mixer power amplifier loudspeaker	op-amps gain calculations G = VOUT / VIN inverting G = - RF / R1 non-inverting G = 1 + RF / R1 summing VOUT = - RF ( V1 / R1 + V2 / R2 + ... ) summing mixer circuit comparator if (V+ > V-) VOUT = V+S if (V+ < V-) VOUT = V-S voltage follower VOUT = VIN gain-frequency graph measure bandwidth from graph gain bandwidth compromise I/O voltage-time graphs normal clipping distortion typical amplifier signal source preamplifier mixer power amplifier loudspeaker bandwidth distortion slew rate slew rate = Δ VOUT / Δ t clean sine wave minimum slew rate = 2 π f Vp ideal op-amp compare with a real one V+ - V- = 0 unless saturated virtual earth comparator bridge circuit balance input impedance non-inverting = infinity comparator = infinity summing/inverting = R1 bandwidth is frequency range where VOUT >= VMAX / √2 gain bandwidth product	op-amps gain calculations G = VOUT / VIN inverting G = - RF / R1 non-inverting G = 1 + RF / R1 summing VOUT = - RF ( V1 / R1 + V2 / R2 + ... ) summing mixer circuit comparator if (V+ > V-) VOUT = V+S if (V+ < V-) VOUT = V-S voltage follower VOUT = VIN gain-frequency graph measure bandwidth from graph gain bandwidth compromise I/O voltage-time graphs normal clipping distortion typical amplifier signal source preamplifier mixer power amplifier loudspeaker bandwidth distortion slew rate slew rate = Δ VOUT / Δ t clean sine wave minimum slew rate = 2 π f Vp ideal op-amp compare with a real one V+ - V- = 0 unless saturated virtual earth comparator bridge circuit balance input impedance non-inverting = infinity comparator = infinity summing/inverting = R1 bandwidth is frequency range where VOUT >= VMAX / √2 gain bandwidth product
GCSE, AS and A Level	AS and A Level	A Level
capacitors farad coulomb	capacitors farad coulomb capacitance definition from C = Q / V Q = C V V = Q / C series CT = 1 / ( 1 / C1 + 1 / C2 + ... ) CT = C1 C2 / (C1 + C2 ) parallel CT = C1 + C2 + ...	capacitors farad coulomb capacitance definition from C = Q / V Q = C V V = Q / C series CT = 1 / ( 1 / C1 + 1 / C2 + ... ) CT = C1 C2 / (C1 + C2 ) parallel CT = C1 + C2 + ...
GCSE, AS and A Level	AS and A Level	A Level
timing period frequency f = 1 / T RC Circuit capacitors charging discharging voltage time graph 555 timer monostable T = 1.1 R C astable f = 1.44 / ( ( R1 + 2R2 ) C ) mark-space ratio TON / TOFF = ( R1 + R2 ) / R2 measure amplitude period	timing period frequency f = 1 / T RC Circuit capacitors charging discharging voltage time graph 555 timer monostable T = 1.1 R C astable tH = 0.7 ( R1 + R2 ) C tL = 0.7 R2 C f = 1.44 / ( ( R1 + 2R2 ) C ) mark-space ratio TON / TOFF = ( R1 + R2 ) / R2 measure amplitude period RC time constant = RC graphs logarithmic axes T50% = 0.69 R C T63% = R C = (T37% discharging) T66% = 1.1 R C (555 mono) T100% = 5 R C charging VC = V0 ( 1 - e(-1 / RC) ) t = - R C ln( 1 - VC / V0 ) discharging VC = V0 e(- R C) t = - R C ln( VC / V0 ) RC de-bouncing Schmitt trigger astable F ≈ 1 / (R C )	timing period frequency f = 1 / T RC Circuit capacitors charging discharging voltage time graph 555 timer monostable T = 1.1 R C astable tH = 0.7 ( R1 + R2 ) C tL = 0.7 R2 C f = 1.44 / ( ( R1 + 2R2 ) C ) mark-space ratio TON / TOFF = ( R1 + R2 ) / R2 measure amplitude period RC time constant = RC graphs logarithmic axes T50% = 0.69 R C T63% = R C = (T37% discharging) T66% = 1.1 R C (555 mono) T100% = 5 R C charging VC = V0 ( 1 - e(-1 / RC) ) t = - R C ln( 1 - VC / V0 ) discharging VC = V0 e(- R C) t = - R C ln( VC / V0 ) RC de-bouncing Schmitt trigger astable F ≈ 1 / (R C )
GCSE, AS and A Level	AS and A Level	A Level
interfacing analogue digital conversion using transistor (npn) MOSFET comparator Schmitt inverter de-bouncing analogue hysteresis	interfacing analogue digital conversion using transistor (npn) MOSFET comparator Schmitt inverter de-bouncing analogue hysteresis signal conditioning voltage dividers photosensitive devices ntc thermistors switches	interfacing analogue digital conversion using transistor (npn) MOSFET comparator Schmitt inverter de-bouncing analogue hysteresis signal conditioning voltage dividers photosensitive devices ntc thermistors switches
GCSE, AS and A Level	AS and A Level	A Level
microcontroller (PIC) programmable integrated circuit interfacing inputs outputs programming flowchart applications vehicles domestic appliances advantages flowcharts start/end process input/output decision/yes/no loop	microcontroller (PIC) programmable integrated circuit interfacing inputs outputs programming flowchart applications vehicles domestic appliances advantages flowcharts start/end process input/output decision/yes/no loop	microcontroller (PIC) programmable integrated circuit interfacing inputs outputs programming flowchart assembler language applications vehicles domestic appliances advantages flowcharts start/end process input/output decision/yes/no loop structure programmable memory input ports output ports CPU clock reset interrupts and polling external device request service on request
GCSE, AS and A Level	AS and A Level	A Level
	power supplies rectification half wave full wave regulation line ? load ? Zener diode alone with emitter follower ? with non-inverting amplifier ? smoothing capacitors ripple voltage Vr = 1 / ( fr C ) VOUT load graph	power supplies rectification half wave full wave regulation line load Zener diode alone with emitter follower with non-inverting amplifier smoothing capacitors ripple voltage Vr = 1 / ( fr C ) VOUT load graph non-inverting amplifier gain equation VL ≈ VZ ( 1 + RF / R1 )
A Level	A Level	A Level
AC Circuits and Passive Filters RC and LC circuits resistive loads use V-t, I-t and P-t graphs impedance of passive filters high-pass low-pass band-pass RMS and Peak series circuit impedance XC = 1 / ( 2 π f C ) XL = 2 π f L Z = √( R2 + X2 ) passive RC filters recognise analyse design draw circuits graphs linear-log log-log buffering passive LC filter (tuned circuit) resonant frequency f0 - 1 / ( 2 π √( L C ) ) dynamic resistance RD = L / ( rL C ) Q factor Q = f0 / bandwidth Q = 2 f0 L / rL	signal conversion digital to analogue analogue to digital ADC compare comparator digital ramp flash ADC priority encoders comparators 2n - 1 calculation DAC summing circuit specification signals communications microprocessors digitise audio - ramp video - flash sampling rate bit rate resolution = i/p voltage range / 2n	communication systems meaningful information transmitted from A received at B structure information source transmitter/encoder transmission medium amplifier/regenerator receiver/decoder information destination wireless transmission digital communication optical communication calculate bandwidth data rate gain noise distortion bandwidth (bw) data rate information-carrying capacity number of channels NCH = available bw / channel bw max data rate = 2 x available bw multiplexing many signals one transmission channel one transmission medium frequency division multiplexing time division multiplexing filter limit information signal bw decibel scale power gain attenuation (power loss) Gdb = 10 log10 ( POUT / PIN ) combined gain of several stages signal to noise ratio power and voltage SNRdb = 10 log10 ( PS / PN ) SNRdb = 20 log10 ( VS / VN ) attenuation in db SNR in db
A Level	A Level	A Level
wireless transmission radio spectrum LF, MF, HF, VHF, UHF, SHF frequency channels data transmission bandwidth requirements availability calculations amplitude modulation (AM) modulation % depth m% = 100 ( Vmax - Vmin ) / ( Vmax - Vmin ) frequency modulation (FM) modulation index β = Δf0 / f1 transmitted bandwidth (bw) bw = 2 ( Δf0 + f1 ) bw = 2 ( 1 + β ) f1 waves electromagnetic sound λ = wavelength f = frequency c = speed of the wave c = speed of light (radio) c = f λ modulation graphs, sine wave AM FM	instrumentation instrumentation amplifiers op-amps difference amplifier VOUT = VDIFF ( RF / R1 ) bridge circuits thermistors strain gauges sensing rotational speed slotted discs sensing angular position encoded discs Binary code Gray code advantage logic system process slotted disc output process encoded discs output	digital communication types of modulation (graphs) pulse code (PCM) transmitter block diagram low pass filter sampling gate sampling clock ADC PISO shift register PISO clock receiver block diagram Schmitt trigger SIPO shift register SIPO clock DAC low pass filter pulse amplitude (PAM) pulse position (PPM) regeneration of digital signals Schmitt trigger circuit Nyquist theorem fSampling = 2 fMax Signal Frequency time division multiplexing (TDM) improved PCM link capacity bit rate (br) number of channels Nchannels br = fSampling x Nbits per sample x Nchannels
A Level	A Level	A Level
optical communication convert signals electrical optical LED LASER photodiode glass fibres refractive index total internal reflection single-mode multi-mode dispersion attenuation latency radiation losses	high power switching DC loads AC loads thyristor DC characteristics holding current minimum gate voltage minimum gate current capacitor commutation diac RC network AC phase control circuit graphs triac RC network AC phase control circuit graphs phase shift supply and capacitor voltage Φ = tan-1 ( R / XC ) advantages over transistor MOSFET relay	audio systems amplifier preamplifier power amplifiers push-pull mixer summing amplifier op-amp active filters inverting first order tone control bass boost treble boost bass cut treble cut break frequency fb - 1 / ( 2 π R C ) multi-stage voltage preamplifier bandwidth gain summing amplifier emitter follower VOUT = VIN - 0.7 source follower VOUT = VIN - 3 but it depends on the MOSFET loudspeaker maximum power transfer theorem push-pull power amplifier emitter follower source follower maximum power PMAX = VS2 / ( 8 RL ) graphs and waveforms active filter frequencies emitter follower source follower push-pull cross over distortion clipping/limiting/saturation reduce distortion biasing negative feedback slew rate distortion

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