3.4 Electronics & Devices
Key Takeaways
- A silicon diode conducts when forward-biased above roughly 0.7 V and blocks current when reverse-biased.
- A BJT in active mode has collector current I_C = beta * I_B; a MOSFET in saturation has drain current that depends on the square of (V_GS - V_th).
- Ideal op-amp golden rules: no current flows into the inputs, and negative feedback forces V+ = V- (the virtual short).
- An inverting amplifier has gain -R_f/R_in; a non-inverting amplifier has gain 1 + R_f/R_in.
- An op-amp integrator output is the time integral of the input scaled by -1/(R*C).
Diodes and rectification
A diode conducts current in one direction. In the common constant-voltage-drop model, a silicon diode is ON (a 0.7 V drop, forward) or OFF (open, reverse). To analyze, assume a state, solve, and confirm the assumption is consistent (forward current positive, or reverse voltage negative).
Key uses:
- Half-wave rectifier: passes one polarity of an AC waveform.
- Full-wave bridge rectifier: four diodes convert both half-cycles to one polarity; output ripple is smoothed by a filter capacitor.
- Zener diode: operated in reverse breakdown at a fixed V_Z to regulate voltage.
For an ideal diode model the forward drop is neglected (0 V); FE problems usually specify which model to use.
Bipolar junction transistor (BJT)
A bipolar junction transistor (BJT) has three regions of operation:
- Cutoff: both junctions reverse-biased, transistor off (I_C = 0), used as an open switch.
- Active (forward-active): base-emitter forward, base-collector reverse; acts as an amplifier with I_C = beta * I_B and I_E = I_C + I_B = (beta + 1) * I_B.
- Saturation: both junctions forward-biased; acts as a closed switch with small V_CE(sat).
The current gain beta (also h_FE) typically ranges from about 50 to 250. The base-emitter junction drop V_BE is about 0.7 V when conducting.
Metal-oxide-semiconductor field-effect transistor (MOSFET)
A MOSFET is voltage-controlled (gate draws essentially no DC current). For an n-channel enhancement MOSFET with threshold voltage V_th:
- Cutoff: V_GS < V_th, no drain current.
- Triode (ohmic): V_DS < V_GS - V_th, acts like a voltage-controlled resistor.
- Saturation (active): V_DS >= V_GS - V_th, I_D = (k/2)*(V_GS - V_th)^2, the square-law region used for amplification.
The quantity (V_GS - V_th) is the overdrive voltage. Because the gate is insulated, MOSFETs have very high input impedance, which is why CMOS dominates digital logic.
Ideal op-amp golden rules and configurations
An operational amplifier (op-amp) has very high open-loop gain and high input impedance. With negative feedback, two golden rules apply:
- No current flows into either input (infinite input impedance).
- The inputs are forced to the same voltage, V+ = V- (the virtual short; a virtual ground when V+ is grounded).
Apply these with KCL at the inverting node to derive every standard circuit.
| Configuration | Output / Gain |
|---|---|
| Inverting | V_out = -(R_f/R_in) * V_in |
| Non-inverting | V_out = (1 + R_f/R_in) * V_in |
| Voltage follower (buffer) | V_out = V_in (gain = 1) |
| Summing (inverting) | V_out = -R_f*(V_1/R_1 + V_2/R_2 + ...) |
| Difference (subtractor) | V_out = (R_f/R_in)*(V_2 - V_1) for matched resistors |
| Integrator | V_out = -(1/(R*C)) * integral of V_in dt |
| Differentiator | V_out = -R*C * dV_in/dt |
The non-inverting gain can never be less than 1; the inverting gain is negative (it inverts polarity).
An inverting op-amp amplifier uses R_in = 2 kohm and R_f = 20 kohm. If the input is +0.5 V, what is the output voltage?
A BJT in the forward-active region has a base current of 20 microamps and beta = 100. What is the collector current?