Analog Electronics and Circuits

power is absorbed in case of semiconductor devices

current direction should oppose voltage to make power -ve for example breakdown voltage should oppose the direction of flow of current

  • measuring devices

    • iron voltmeter

      RMS

    • magnetic

  • capacitors

    voltage and current across capacitor is zero → short circuit

    capacitors doesn’t allow abrupt changes : \(V_c(t^+)=V_c(t^-) = V_c(t)\)

  • inductors

    voltage and current across inductor is zero → open circuit

  • diodes

    • clampers

      • negative clamper

        \(V_{in_{max}} > 0\) for diode to conduct

      • positive clamper

        \(V_{in_{min}} < 0\) for diode to conduct

    • rectifiers

      \(\text{form-factor} = \dfrac{x_{rms}}{x_{avg}}\)

  • transistor

    • transistor biasing

      \(S = \dfrac{\partial I_C}{\partial I_{C_O}} = \dfrac{\beta + 1}{1 - \beta\dfrac{\partial I_B}{ \partial I_C}}\)

      \(I_{E} = I_C+I_B\)

      \(I_C = \beta I_B + (1+\beta) I_{C_{O}}\)

      \(\beta = \frac{I_C}{I_B}\) ; common emitter gain (base as input and collector as output)

      \(\alpha = \frac{I_C}{I_E}\) ; common base gain

      If \(\beta\) is high, \(I_C = I_E\) and \(I_B = 0\)

      • collector with base bias with RE

      • voltage divider bias with RE

    • small signal analysis

      • steps

        1. turn off all dc sources and short all capacitors (small signal equivalent)

        2. calculate parameters such as \(r_\pi, r_e, g_m\)

        3. replace by model

        • calculate

          • \(r_i, R_i\)

          • \(r_o, R_o\) by putting \(v_s = 0\)

          • \(A_v = \dfrac{v_o}{v_s}\)

          • \(A_I = \dfrac{i_l}{i_i}\)

      \(g_m = \dfrac{I_c}{V_T}\)

      \(r_\pi = \dfrac{\beta}{g_m}\)

      \(r_o= \dfrac{V_A}{I_C} = \dfrac{1}{\lambda I_C}\)

      \(\boxed{\dfrac{v_{be}}{i_b} = h_{ie} = (1+\beta)r_e = r_\pi}\)

      \(\boxed{\dfrac{i_{c}}{i_b} = h_{fe} = \beta = g_mr_\pi}\)

      • h - parameter

        \(v_{be} \approx h_{ie} i_b\)

        \(i_c \approx h_{fe} i_b\)

      • \(r_e\) - model

        \(r_e = \dfrac{V_T}{I_E}\)

        \(v_{be} = i_b (1+\beta) r_e\)

        \(r_i = \dfrac{v_{be}}{i_b} = (1+\beta)r_e\)

      • \(\pi\) -model

        \(i_c = \dfrac{I_C}{V_T} v_{be} = g_m v_{be}\)

        \(\boxed{\dfrac{v_{be}}{i_b} = \dfrac{\beta}{g_m} = r_\pi}\)

      • CE with \(R_{E}\)

        \(R_i = (r_{\pi} + \beta R_E) || R_B\)

        \(A_v = \dfrac{-g_m R_C}{1 + g_m R_E}\)

    • multistage

      • CE-CE and CE-CC → cascade

      • CE-CB → cascode

      • CC-CC → Darlington pair

  • op-amp

    • differential amplifier

      • differential mode

        \(A_{v_1} = A_{v_2} = -g_m R_c\)

        \(A_d = \dfrac{v_o}{v_{id}} = g_m R_c\)

      • common mode

        \(A_{v_1} = A_{v_2} = A_c =\dfrac{-g_m R_c}{1 + 2 g_m R_E}\)

      \(\text{CMRR} = \biggm\vert \dfrac{A_d}{A_c} \biggm\vert = 1 + 2\cdot g_m R_E\)

      \(v_{c} = \dfrac{v_1 + v_2 }{2}\)

      \(v_{id} = v_1 - v_2\)

      \(v_o = A_d\cdot v_{id} + A_c \cdot v_{c}\)