## Semiconductor Devices And Communication Systems Synopsis

**Conductivity (σ) of a conductor:** This is given by

∴ \(\sigma=\frac{\text { current density }(j)}{\text { electric field }(E)}=\frac{n e v}{E}=n e \mu\)

where μ = mobility of electrons and v = drift speed of electrons.

**The conductivity of a semiconductor:** This is given by

∴ [laytex]\sigma=n_{\mathrm{e}} e \mu_{\mathrm{e}}+n_{\mathrm{h}} e \mu_{\mathrm{h}}[/latex]

where the subscripts e and h respectively represent electrons and holes.

**Resistance of a p-n junction:**

- Static (or DC) resistance = \(R=\frac{V}{I}\), where V = operating voltage.
- Dynamic (or AC) resistance = \(r=\frac{\Delta V}{\Delta I}\)

This is the reciprocal of the slope of the I-V characteristic.

The emitter, collector, and base currents in a transistor are related by the equation I_{e} = I_{c} + I_{b}.

**α- and β-parameters of a transistor:** These two parameters are given by

∴ \(\alpha=\frac{I_{\mathrm{c}}}{I_{\mathrm{e}}} \text { and } \beta=\frac{I_{\mathrm{c}}}{I_{\mathrm{b}}}=\frac{\alpha}{1-\alpha}\)

Voltage gain = \(\frac{V_{\text {out }}}{V_{\text {in }}}=\frac{I_{\mathrm{c}} R_{\mathrm{L}}}{I_{\mathrm{b}} R_{\mathrm{BE}}}=\beta\left(\frac{R_{\mathrm{L}}}{\dot{R}_{\mathrm{BE}}}\right)\)

Power gain = (voltage gain)(current gain)

⇒ \(\beta\left(\frac{R_{\mathrm{L}}}{R_{\mathrm{BE}}}\right)\left(\frac{I_{\mathrm{c}}}{I_{\mathrm{b}}}\right)=\beta^2\left(\frac{R_{\mathrm{L}}}{R_{\mathrm{BE}}}\right)\)

A logic gate is an electric device that performs a logical operation on one or more binary inputs and produces a single binary output.

**Symbols and Boolean expressions for basic logic gates and their truth tables:**

**(1) OR gate:**

**(2) AND gate:**

**(3) NOT gate:**

**(4) NOR gate:**

**(5) NAND gate:**

**Range:** The maximum distance from the transmitter (which sends the signals) to the receiving station (where the signals are received) with sufficient strength is called the range. It is given by

⇒ \(d=\sqrt{2 R_{\mathrm{E}} h}\)

where R_{E} = the earth’s radius and h = height of the antenna.

**Maximum line-of-sight (LoS) distance:**

⇒ \(d=\sqrt{2 R h_1}+\sqrt{2 R h_2}\)

where h_{1} and h_{2} are the heights of the transmitting and receiving antennas.

**Modulated and carrier waves:**

(1) Carrier wave: e_{c} = E_{c} cos ω_{c}t.

(2) Modulating signal: e_{m} = E_{m} cos ω_{m}t.

(3) Amplitude of the modulated wave = E_{c} + E_{m} cos ω_{m}t.

(4) Modulated wave:

e = (E_{c} + E_{m} cos ω_{m}t) cos ω_{c}t

⇒ \(E_{\mathrm{c}}\left(1+\frac{E_{\mathrm{m}}}{E_{\mathrm{c}}} \cos \omega_{\mathrm{m}} t\right) \cos \omega_{\mathrm{c}} t\)

⇒ E_{c} (1 + m cos ω_{m}t) cos ω_{c}t,

where \(m=\frac{E_m}{E_c}\) is the modulation index

∴ \(E_{\mathrm{c}} \cos \omega_{\mathrm{c}} t+\frac{m E_{\mathrm{c}}}{2} \cos \left(\omega_{\mathrm{c}}-\omega_{\mathrm{m}}\right) t+\frac{m E_{\mathrm{c}}}{2} \cos \left(\omega_{\mathrm{c}}+\omega_{\mathrm{m}}\right) t\)