Circuits and analog electronics - complete review of notes

1.1 Circuits and circuit models

The circuits are circuits made of electrical equipment and components that are connected in a certain way. The circuit model is an approximation of the actual circuit using ideal components (R, L, C, power, etc.). Three components of circuits:** power supply** (provision of electricity),** load** (consumption of electricity),** middle link** (conductor, switch etc.).

1.2 Basic physical mass of circuits

Electricity

• Definitions:$i = \frac{dq}{dt}$Unit Amber (A)
• ** Reference orientation**: artificially set positive direction
• The actual direction corresponds to the reference direction

voltage

• Definitions:$u_{ab} = \frac{dW}{dq}$,unit volts
• Direction: High, low, low.
• Reference polarity is arbitrary

Level

• Definition: voltage of a point to a reference point (ground, 0V)
• The level is ** relative** and the voltage is 2 points. Bad
• The short lead between the level points doesn’t affect the circuit.

Power and power/load judgement

• $P = U \times I$, units & watts
• Contribution reference orientation (electricity flow from voltage ”+”): P>0 absorbent load; P<0 sends out power
• ** Non-relative orientation**: P>0 sending power; P<0 absorbent load

** [Text example 1-1]** Verify power balance and judge the nature of the component:

• Component 1: P = 5V x 2A = 10W (unconnected, P>0)
• Component 2: P=2Vx2A=4W (association, P>0)
• Component 3: P=−2Vx2A=−4W (unconnected, P<0) → Absorption of 4W, load
• Total dispatch = total absorption power balance

1.3 Resisting, capacitating, sensory components

Electrical resistance

• Line electrical resistance:$u = Ri$Vulcan properties are transient lines
• Electrical $G = 1/R$Unit S
• Power:$P = i^2R = u^2/R$(continuously positive, energy-consuming components)

Electric

• $q = Cu$，$i = C\frac{du}{dt}$
• $u_C(0^+) = u_C(0^-)$: Capable voltage cannot mutate
• Storage:$W_C = \frac{1}{2}Cu^2$
• ** When the flow is steady**

Electricity

• $\Psi = Li$，$u = L\frac{di}{dt}$
• $i_L(0^+) = i_L(0^-)$: Electromagnetic currents cannot mutate
• Storage:$W_L = \frac{1}{2}Li^2$
• ** Short circuit**

1.4 Reference direction for voltage and currents

The voltage reference direction has three expressions: positive and negative poles, double subscripts, and solid line arrows. There are two types of current reference directions: solid line arrows, double subscripts.

Contribution reference orientation: current flow from voltage ”+” extreme. Once the direction is determined, the analysis shall not change.

1.5 Om Law

• Related direction:$U = RI$ or $I = GU$
• Non-related orientation:$U = -RI$
• ** Total circuit Orm Law**:$I = E/(R+r)$(r is internal to the power supply)

1.6 Kilhoff Law

KCL.

• $\sum I_{入} = \sum I_{出}$ or $\sum I = 0$
• Nature: Charge constant.
• ** Extension**: closed face = broad node

** [Text example 1-2]** Column node KCL equation gradually solves the currents of the roads $I_1$~$I_6$

KVL.

• $\sum U = 0$(Closed circuit, voltage algebra and zero)
• Select any direction to go around, refer to the same direction to go around
• Expression III:$\sum RI = \sum U_s$

[Text example 1-3]** Known $U_{ab}=20V, U_{bc}=10V$ Wait, please. $U_{bd}$ and $U_{ed}$

1.7 Concept and calculation of the electrical level

Level calculation step

1. Selected point of reference (Land, 0V)
2. From reference point to target point along the circuit
3. Electro-retardation (-IR); retrenchment (+IR)
4. Ex-voltage source: U from + to - →; U from - to + 升

2.1 Consistency of resistance

Serial

• $R_{eq} = R_1 + R_2 + \cdots$
• Pressure formula:$U_k = U \times \frac{R_k}{\sum R}$

Together.

• $\frac{1}{R_{eq}} = \frac{1}{R_1} + \frac{1}{R_2} + \cdots$
• Two parallels:$R_{eq} = \frac{R_1 R_2}{R_1+R_2}$
• Diversion formula:$I_k = I \times \frac{G_k}{\sum G}$

2.2 Equivalent transformation of resistance Y-Δ

Y → Δ：$R_{ab} = \frac{R_a R_b + R_b R_c + R_c R_a}{R_c}$(symmetrical rotation)

Δ → Y：$R_a = \frac{R_{ab} \times R_{ca}}{R_{ab} + R_{bc} + R_{ca}}$

Symmetric status:$R_Y = \frac{1}{3}R_{\Delta}$

2.3 Two models of power supply and their equivalent transformation

| Change, tact, formula, tact, intangibility, tact. |---|---|---| | Power source, current source. $I_s = U_s/R$ R-Among | Power source, voltage source. $U_s = I_s \times R$ |R series

⚠️ Only external circuits are equivalent! The ideal power source (R=0) cannot transform the current source; the ideal current source (R=∞) cannot transform the power source.

2.4 Secondary and grid current methods

• Strategic current method: b each feeder (n−1) KCL + [b−(n−1)] KVL
• nethole current method: unknown at gridhole current, one KVL per hole

2.5 Collapse Theorem

** Theoretically**: In linear circuits, any response = the algebra and the response when the independent source acts alone.

** Steps**

1. Only one single source at a time, the rest of the power is short, the current is open.
2. Calculate points separately
3. Algebra and superseding

** only linear circuits!

2.6 David Nam Theorem

** Theoretically**: any linear active second-end network Source $U_{oc}$ + Barrier $R_{eq}$ Serial.

| Parameters Parameters |---|---| | $U_{oc}$ Cut off the outside circuits, open the port. | $R_{eq}$ | 1-to-0: Independent source fully zero back port resistance 2$U_{oc}/I_{sc}$ Law

Maximum Power Transfer Theorem

• $R_L = R_{eq}$ Maximum power per hour
• $P_{max} = \frac{U_{oc}^2}{4R_{eq}}$

2.7 Controlled power sources

Four types: VCVS (voltage-controlled voltage), VCCS (voltage-controlled current), CCLVS (flow-controlled voltage), CCS (flow-controlled current). Controlled sources in the superseding theorem and the Davianorian theorem** cannot be avoided**.

3.1 Basic concepts of dynamic circuits

• Stable state: voltage currents do not change over time
• Temporarily (transitional process): from one steady state to another
• ** Switching**: switch action, circuit state changes caused by mutation of parameters

3.2 Alternative rules

| Component Rules Reason |---|---|---| | Electricity $u_C(0^+) = u_C(0^-)$ Power field energy $\frac{1}{2}Cu^2$ Can’t mutate. | Electromagnetic $i_L(0^+) = i_L(0^-)$ Magnetic field energy. $\frac{1}{2}Li^2$ Can’t mutate.

Other$i_C$、$u_L$、$u_R$、$i_R$It can mutate.

3.3 Determination of initial and steady-state values

Initial value [v]

1. Please $u_C(0^-)$ or $i_L(0^-)$(Pre-Road steady)
2. 0+ value for rerouting
3. Draws 0+ Equivalent Circuits: Capacitivity Power Sources, ISP Sources
4. Initial value for other quantities

Steady state value (%2)$t \to \infty$）

• Capacitive ** Open road**$i_C = 0$）
• ** Short circuit**$u_L = 0$）

3.4 Time constant

| It’s the circuit. It’s the flat. |---|---|---| | RC | $\tau = R_{eq}C$ |(s) | | RL | $\tau = L/R_{eq}$ |(s) |

$R_{eq}$: Davidnan Equivalent Absorption from C or L.

And the physical significance: responding to decay to the initial value of 36.8% takes time.$t=3\tau\sim5\tau$ The subsequent provisional status is essentially over.

3.5 The temporary process of the RC circuit

Zero input response (discharge)

• $u_C(t) = u_C(0^+) e^{-t/\tau}$
• $i(t) = \frac{u_C(0^+)}{R} e^{-t/\tau}$

Zero status response (charged)

• $u_C(t) = U_s(1 - e^{-t/\tau})$
• $i(t) = \frac{U_s}{R} e^{-t/\tau}$

3.6 Three-Element Method

** General formula**: $$f(t) = f(\infty) + [f(0^+) - f(\infty)] e^{-t/\tau}$$

Three elements:$f(0^+)$ initial value,$f(\infty)$ steady-state,$\tau$ Time constant

A template for solution: 1 request $u_C(0^+)$ Two. $u_C(\infty)$ Three. $\tau$ 4-generation formula

Scope of application:** First-order linear circuit**

3.7 Micro- and cumulation circuits

Microcircuit

• Condition: Output from a resistance end,$\tau \ll t_w$
• Rectangular pulse.

Quantum circuit

• Condition: Output from the capacitive end,$\tau \gg t_w$
• $u_o = \frac{1}{RC}\int u_i dt$

4.1 Basic concepts of sine

Three elements

$$u(t) = U_m \sin(\omega t + \varphi)$$

• Valid value:$U = U_m/\sqrt{2} \approx 0.707U_m$
• 50Hz:$\omega = 314$ rad/s

4.2 Phase expression of the sine

• ** phase**: sine $u = \sqrt{2}U\sin(\omega t+\varphi)$ → $\dot{U} = U\angle\varphi$(Mixed number)
• Phase ≠ Sine, just a tool to calculate
• $j$ = 90° reverse clockwise (upfront),$-j$ = clockwise 90° (delayed)

4.3 Sine exchange circuits for single parameters

| Shape Pyramid Pyramid Pyramid Pyramid Pyramid Pyramid Pyramid |---|---|---|---| | R | $\dot{U} = R\dot{I}$ P = I2R, Q = 0 | L | $\dot{U} = j\omega L\dot{I}$ |U +I2X L| | C | $\dot{U} = -j\frac{1}{\omega C}\dot{I}$ | U delays I 90° P=0, Q=-I2X C|

• $X_L = \omega L = 2\pi fL$(exhales)
• $X_C = 1/(\omega C)$(Stammering)
• Direct: f=0 x L=0 (short circuit), X C= open road

4.4 RLC serial circuit

$$Z = R + j(X_L - X_C) = R + jX = |Z|\angle\varphi$$

• $|Z| = \sqrt{R^2+(X_L-X_C)^2}$
• $\varphi = \arctan\frac{X_L-X_C}{R}$

4.5 Consistency of resistance

• Serial:$Z_{eq} = Z_1 + Z_2 + \cdots$
• Together:$Y_{eq} = Y_1 + Y_2 + \cdots$（$Y=1/Z$）
• Two parallels:$Z_{eq} = \frac{Z_1 Z_2}{Z_1+Z_2}$

4.6 Reactivate circuits

Convergence conditions

$X_L = X_C$i.e. $\omega L = 1/(\omega C)$

Interson frequency

$$f_0 = \frac{1}{2\pi\sqrt{LC}}$$

Serial resonance

| It’s a special feature. |---|---| | $Z_0$ =R (** minimum**)| | $I_0$ = = U/R(** max**)| | $U_L, U_C$ = QU(Q2x!) | | Q | $Q = \omega_0 L/R$ | | BW | $f_0/Q$ |

Convergence.

| It’s a special feature. |---|---| | $Z_0$ | max. | | $I_0$ | Smallest | Subway current = QI0 (Q+ total current) |

4.7 Power

| Power, | formula, ** unit, ** constant? ** Ta-da |---|---|---|---| | P (decent) $UI\cos\varphi$ W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-W-T-T-R-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T-T- | Q (no merit) $UI\sin\varphi$ I’m sorry. | “S” $UI = \sqrt{P^2+Q^2}$ ** VA ** Unsatisfactory**

• Power factor:$\cos\varphi = P/S$
• Upgrading methods: and connected capacitors

7.1 Semiconductor basic knowledge

Semiconductor

• Pure Silicon (Si) or Ge (Ge) single crystal
• Motivated by this phenomenon, the free electronics + the void pair

impurity semiconductor

| Type of cylindrical blended into cylindrical cylindrical cylindrical |---|---|---|---| | Type N 5 price (phosphorus P) | Type P, 3-priced (BB)

7.2 PN Conclusion

Form

P- and N-type contact, proliferation movement, space charge zone (depletion level) built-in power fields, dynamic balance

One-way conductivity

| It’s just, you know, it’s just, you know, it’s— it’s— it’s— it’s—it’s—it’s—it’s—it’s—it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s-it’s—it’s-it’s-it’s-it’s-it. |---|---|---| | (P+, N-) Twist | Inverted (P-, N+) glyphs thickened, glyphs very small

• Positive Guidance: Siliconium 0.7V, 锗≈0.3V
• Reverse saturation current $I_S$: Temperature approximately double 10°C per litre

7.3 Semiconductor diodes

Vulcan properties

| Area conditions |---|---|---| | Dead zone 0 < U < 0.5V (silica) | i ≈ 0 < | Positive Wizard | > 0.5V | | exponential growth | Inverse cut-off -U BR < U < 0 i≈I S| | <-U BR | |

Secondary circuit analysis

• Ideal model: Guide U D=0, cut-off I D=0
• Constant pressure-relief model: conductive U D=0.7V (silica)

7.4 Steady diodes

• ** Worked in a reverse blowout zone! **
• Plus reverse voltage ≥ U Z → End voltage stabilized at U Z
• System-restricted current resistance R
• Dynamic electrical resistance $r_Z = \Delta U_Z/\Delta I_Z$The smaller the better.

Steady circuit analysis

U_i → R(限流) → D_Z(稳压管,反向) ∥ R_L(负载)

** Analytical steps**:

1. Confirm. $U_i > U_Z$(Knocking)
2. $U_O = U_Z$
3. $I_R = (U_i-U_Z)/R$，$I_L = U_Z/R_L$，$I_Z = I_R-I_L$
4. Inspection $I_{Zmin} \leq I_Z \leq I_{Zmax}$

7.5 Transistors (BJT)

Zoom in.

| NPN zoom in. |---|---| | Launching knots, twilight, twilight. | Zero, zero, zero, zero.

Three workspaces

| Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone Zone and Zone B Zone |---|---|---|---| | ** Zoom in** $I_C = \beta I_B$ | | Saturation, positive, positive, positive. $I_C < \beta I_B$ | | End of period $I_C \approx 0$ |

Three groups

| Catalyzine, voltage, voltage, voltage, voltage. |---|---|---|---| | CE | (reverse) | most commonly used | | Co-existing (CC/Sport) |1 (Same)| | CB | (same)

7.6 Field effect tubes (FET)

Compare to BJT

Classification: JFET (concentrated), MOSFET (insulated, enhanced/depleted)

7.7 Special diodes

We’re gonna have to check the test quickly.