Semi-conductor & Electronics

Based on the provided sources and our conversation history, here are the key concepts,
explanations, and formulae you should review:

PN Junction Diodes Circuits

Diode Definition and Basic Operation:

A diode is a dipole with two terminals: the anode (A) and the cathode (C or K).
It generally allows current to pass in one direction (forward) and blocks it in the other
(reverse).
Its operation is similar to a switch that allows current flow in only one direction.
The diode becomes conductive (or passing) when the potential of the anode (A) is
higher than the potential of the cathode (C or K). This requires applying an external
voltage.
Diode Models:
Ideal Diode:
In forward bias (VAK = 0), I > 0: equivalent to a closed switch.
In reverse bias (VAK < 0), I = 0: equivalent to an open switch.
Perfect Diode:
In forward bias (VAK = Vd), I > 0: equivalent to a perfect voltage source Vd.
In reverse bias (VAK < Vd), I = 0: equivalent to an open switch.
Real Diode:
In forward bias (VAK = Vd), I > 0: equivalent to a voltage source Vd with
internal resistance (Rd = ΔVAK/ΔI).
In reverse bias (VAK < Vd), I = 0: equivalent to an open switch.
Diode with Threshold Voltage (Vd):
If VAK ≤ Vd: The diode is blocked, current I across RL is 0, Vs = 0.
If VAK > Vd: The diode conducts, Vs = Ve - Vd.
Diode Applications:
Rectification Circuits: Convert an alternating voltage into a direct voltage. Used in
power supplies for electronics.
"Single-wave" rectification.
"Double-wave" rectification (Graëtz bridge).
Capacitor filtering: Smoothes a rectified voltage to obtain a more continuous
voltage. A capacitor is placed in bypass at the output of the rectifier bridge.
 Clamping or Limiting Circuits: Prevent a signal from exceeding a certain value.
Example: Zener diodes.
Switching Circuits: Used as switches in digital electronics.
Voltage multiplication (e.g., voltage doubler).
Clipping: Removing part of a signal's amplitude. Rectification is a special case.
Static and Dynamic Characteristics:
Static load line I = f(V): Graphical representation of the current-voltage relationship
under DC conditions.
Operating point (Bias point): Steady-state conditions, where voltages and currents
are stable. It is the equilibrium condition where component characteristics (like a
diode's I-V curve) and the circuit's load line intersect.
The operating point P is the intersection between the diode characteristic
(ID=f(V)) and the load line equation ID = (E − V) / R.
Dynamic Regime: Applied voltage varies as a function of time (e.g., AC).
Dynamic Resistance (Small-signal resistance rd): Characterizes the diode's
response to small changes in voltage around a DC operating point in the dynamic
regime. It is the inverse of the slope at the operating point of the I(V) characteristic.
Zener Diode:
Designed to allow current flow in both directions.
In forward bias, behaves like a normal diode.
In reverse bias, if negative voltage increases, reverse current is constant up to a well-
defined voltage (the Zener voltage Vz), at which it increases rapidly – this is the
Zener effect.
The Zener effect occurs at Vz without destroying the diode.
In reverse bias, current can change significantly while voltage stays close to Vz.
Relationship in reverse bias: VAK = Vz + rz * iz.
Maximum power supported: Pmax = Vz * Izmax.
If dynamic resistance rz is neglected, voltage in reverse is constant (Vz).
Application: Stabilizing voltage across a load. The Zener blocks until load voltage
exceeds Vz, then conducts and holds voltage at Vz.
Light Emitting Diode (LED):
A semiconductor device that emits light when forward biased.
Made of special semiconductors like AlInGaP and InGaN.
Working principle: Recombination of electrons and holes produces light. Electrons
falling from the conduction band to the valence band release energy. This energy can
be released as heat (phonons) or light (photons) - the electroluminescence effect.
Color depends on the material used and its dominant emission wavelength.
Transistors (Bipolar Junction Transistor - BJT)

BJT Definition and Structure:

A Bipolar Junction Transistor (BJT) is an active device with 3 connections: the
Emitter (E), the Base (B), and the Collector (C).
Called bipolar because both majority and minority carriers are involved.
Consists of two PN junctions (or diodes) connected in opposite directions.
Two junctions: the Base-Emitter (BE) junction and the Base-Collector (BC)
junction.
Two types: NPN (P-type base between N-type E and C) and PNP (N-type base
between P-type E and C).
Structure is not symmetrical: Emitter heavily doped (injects carriers), Base lightly
doped and thin (transmits carriers, minimizes recombination), Collector collects
carriers.
Arrow in symbol: always on the emitter, points towards the n-type, indicates emitter
current direction.
BJT Currents and Relationships:
Currents: IC (collector current), IB (base current), IE (emitter current).
Kirchhoff's Law: IE = IB + IC.
NPN: positive quantities; PNP: negative quantities.
In linear operation, Base is lightly doped, so IB << IC and IE.
IC ≈ IE.
Current amplification factor (α): IC = α * IE.
Base current amplification factor (β): IC = β * IB.
Relationship between α and β: β = α / (1 - α). Typical values: 0.95 ≤ α ≤ 0.998 means
20 ≤ β ≤ 500.
BJT Operation Regions:
Cutoff Region:
BE junction reverse biased.
BC junction reverse biased.
No current flow. Behaves like an open switch.
IB ≈ 0.
Saturation Region:
BE junction forward biased.
BC junction forward biased.
Transistor is on. Acts like a closed switch.
VCE is very low (VCE = VCEsat).
IC is not proportional to IB.
 Linear (Active) Region:
For NPN: BE junction forward biased (VBE ≥ Vthreshold, ~0.7V for Si).
For NPN: BC junction reverse biased.
Transistor acts as an amplifier.
A small input base current (IB) controls a much larger collector-emitter current
(IC).
IC = β * IB.
IC is independent of VCE (within limits).
VCE is moderate.
Breakdown Region: VCE is large, beyond limits.
BJT Characteristics:
Input Characteristic IB(VBE): In linear mode, similar to a forward-biased diode
characteristic.
Output Characteristic IC = f(VCE): Plotted for constant values of IB. Shows cutoff,
linear, and saturation regions.
Basic Transistor Assemblies (Configurations): Three main configurations based on the
shared electrode:
Common Emitter (CE): Input: IB, VBE. Output: IC, VCE. Shared: Base.
Common Collector (CC): Input: IB, VBC. Output: IE, VEC. Shared: Collector.
Common Base (CB): Input: IE, VEB. Output: IC, VCB. Shared: Emitter.
Darlington Bipolar Transistor:
Combination of two BJTs of the same type. Collectors are common. Driver emitter
connected to output base.
Overall current amplification factor is the product of the individual transistors' factors.
BJT Static Mode (DC Biasing):
Refers to operation in a steady state with constant DC currents and voltages.
The transistor is biased with constant DC values to set its operating point (quiescent
point or Q point).
Biasing ensures the transistor operates in a desired region (active, saturation, or
cutoff).
The operating point is characterized by (VBE0, IB0) and (IC0, VCE0).
Biasing is achieved using voltage sources and resistors.
Static load line is plotted on the transistor characteristics (IC=f(VCE) and IB=f(VBE))
to visualize the operating point.
The intersection of the load line and the transistor's characteristic gives the operating
point.
Example biasing circuits using one voltage source: base resistance RB, resistance
between base and collector, base resistance bridge, base resistance bridge with
 emitter resistance.

Voltage and Current Divider Circuits

Voltage Divider:
Occurs when a voltage is applied to a series combination of resistances.
A series circuit acts as a voltage divider.
Formula: The voltage drop (Vx) across any resistor (Rx) or combination of resistors in
a series circuit is given by: Vx = (Rx / RT) * Vs, where RT is the total series resistance
and Vs is the source voltage.
Current Divider:
Occurs in a parallel circuit, where the total current entering a junction divides among
the parallel branches.
A parallel circuit acts as a current divider.
General Formula: The current (Ix) through any parallel resistor (Rx) is given by: Ix =
(RT / Rx) * IT, where RT is the total parallel resistance and IT is the total current into
the junction.
Formula for Two Parallel Resistors (R1, R2):
Current through R1 (I1): I1 = (R2 / (R1 + R2)) * IT.
Current through R2 (I2): I2 = (R1 / (R1 + R2)) * IT.

Circuit Theorems

Linearity Property:
Describes a linear relationship between cause (input) and effect (output).
Combination of homogeneity and additivity.
Homogeneity: If input is multiplied by a constant, output is multiplied by the same
constant (e.g., Ohm's Law: v=iR, kiR=kv).
Additivity: Response to a sum of inputs is the sum of responses to each input applied
separately (e.g., Ohm's Law: v1=i1R, v2=i2R, (i1+i2)R = v1+v2).
A linear circuit has an output linearly related (directly proportional) to its input.
Superposition Principle:
Applicable to linear circuits.
States that the voltage across (or current through) an element is the algebraic sum of
the contributions from each independent source acting alone.
Steps:
1. Turn off all independent sources except one (voltage source -> short circuit, current
source -> open circuit). Dependent sources are left intact.
2. Find the output due to that single active source.
 3. Repeat for each independent source.
4. Algebraically add all the individual contributions.
Source Transformation:
A tool for simplifying circuits.
Process of replacing a voltage source in series with a resistor by a current
source in parallel with the same resistor, or vice versa.
Relationship: is = vs / R or vs = is * R.
The arrow of the current source points toward the positive terminal of the voltage
source.
Also applies to dependent sources.
Not possible for ideal voltage sources (R=0) or ideal current sources (R=∞).
Thevenin’s Theorem:
Simplifies any linear two-terminal circuit into an equivalent circuit.
The Thevenin equivalent circuit consists of a voltage source VTh in series with a
resistor RTh.
VTh: The open-circuit voltage (voc) at the terminals. VTh = voc.
RTh: The input or equivalent resistance at the terminals when the independent
sources are turned off. RTh = Rin.
If no dependent sources: Turn off independent sources, calculate resistance.
If dependent sources: Turn off independent sources, apply a test voltage (vo) or
current (io) and calculate RTh = vo/io. RTh can be negative if circuit supplies
power.
When a load RL is connected, the circuit is a simple series circuit of VTh, RTh, and RL.
Current through load IL = VTh / (RTh + RL).
Voltage across load VL = (RL / (RTh + RL)) * VTh.
Norton’s Theorem:
Similar to Thevenin's, simplifies a linear two-terminal circuit.
The Norton equivalent circuit consists of a current source IN in parallel with a
resistor RN.
RN: Found the same way as RTh. RN = RTh.
IN: The short-circuit current (isc) through the terminals. IN = isc.
Relationship to Thevenin's: RN = RTh and IN = VTh / RTh. This is source
transformation.
VTh, RTh, and IN can be found using open-circuit and short-circuit tests: VTh = voc,
IN = isc, RTh = voc / isc = RN.
Maximum Power Transfer Theorem:
Concerns maximizing the power delivered to a load from a linear circuit.
 States that maximum power is transferred to the load (RL) when the load
resistance equals the Thevenin resistance (RTh) as seen from the load. RL = RTh.
Power delivered to load: p = (VTh / (RTh + RL))^2 * RL.
Maximum power transferred: pmax = VTh^2 / (4 * RTh). This formula only applies
when RL = RTh.
Millman’s Theorem:
Used to reduce any number of parallel voltage sources to a single equivalent
voltage source.
Equivalent voltage source Eeq in series with equivalent resistance Req.
Eeq = (Σ Ek/Rk) / (Σ 1/Rk), where Ek are the individual source voltages and Rk are
their series resistances. Pay attention to source polarities.
Req = 1 / (Σ 1/Rk).
Substitution Theorem:
Applicable to DC bilateral networks.
If the voltage across and current through a branch are known, that branch can be
replaced by any combination of elements that maintains the same voltage and
current across its terminals.
A known voltage and current can be replaced by an ideal voltage source and ideal
current source, respectively.
Reciprocity Theorem:
Applicable only to single-source networks.
States that the current (I) in a branch due to a single voltage source (E) elsewhere in
the network will equal the current through the branch where the source was located if
the source is moved to the branch where the current was originally measured.
The location of the voltage source and the resulting current can be interchanged
without changing the current value.
Requires the voltage source polarity to correspond to the branch current direction in
both positions.

These concepts cover the fundamentals of diodes, transistors, basic circuit analysis principles,
and circuit theorems presented in the sources.