16-08-2012, 11:45 AM
Elementary Electronic Circuits with a Diode
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THE AIM OF THE COURSE
Lumped linear time-invariant (LLTI) electric circuits do not provide any solution to the following five tasks (see Fig. 1), which are very important in Electrical Engineering:
1) It is impossible to control the circuit transfer function (gain) by an electrical signal, either voltage or current.
2) It is impossible to implement a circuit with a dc gain greater than one.
3) It is impossible to implement a circuit with a power gain greater than one.
4) It is impossible to implement a current source.
5) It is impossible to implement an oscillator (circuit generating a periodic signal), for example, a sine-wave oscillator.
The aim of the course is to solve all the above tasks by using electronic devices: diodes and transistors. To develop and study electronic circuits, we start from elementary circuits, analyze them, and then improve if there is a need.
1. ELEMENTARY ELECTRONIC CIRCUITS WITH A DIODE
Our main aim here is to build a circuit with a gain (not necessarily greater than one) that can be controlled by an electrical signal, either voltage or current. Namely we would like to build a voltage-controlled voltage divider and a current-controlled current divider (homework).
To reach this goal, we first develop physical, mathematical, and finally a graphical model of the diode. Based on the graphical model, we find equivalent electric circuits to replace a diode in an electronic circuit. This will allow us to analyze single-diode electronic circuit by applying electric circuit theory.
1.1. Diode: symbol, physical structure, analytical model and graphical characteristic
The symbol of the diode and its physical structure are given in Fig. 2. To develop a mathematical model of the diode we have to describe the dependence of the diode current, iD, on the diode voltage, vD.
Assuming that the n region is much more heavily doped that the p region, npo >> pno, we neglect the diode current due to the holes and consider only that due to the electrons. Neglecting the small effect of the weak electric field within the p region on the electrons, which are the minor charge carriers in this region, we conclude that the diode current is exclusively due to the diffusion current of electrons:
where jD is the diode current density, A is the diode cross-section area, np(0) is the concentration of the electrons in the p region at x=0 (see Fig. 2), npo is the thermal-equilibrium concentration of the electrons in the p region (when the diode terminals are open circuited), Dn is the diffusion constant of the electrons, q is the charge of the electron, Ln is the diffusion length for the electrons, VT is the thermal voltage, and IDS is the saturation current of the diode.
It is worth noting, that at room temperature
k in (2) is the Boltzmann constant, and T is the absolute temperature. The typical value of IDS is 10 fA. Due to the strong dependence of npo on temperature, the IDS current doubles its value per a 5° increase of the diode temperature.
Based on (1), we draw in Fig. 3 the diode iD-vD characteristic.
1.2. Static and dynamic impedances
Note (see Fig. 4) that the characteristic of the diode is nonlinear whereas that of a resistor is linear. As a result, a diode translates (amplifies) differently static, ID and VD, and incremental (dynamic), dvD≡vd and diD≡id, signals:
Let us denote the incremental signals as small signals. In electronic circuits, static signals usually define operating points of electronic devices to provide a required translation (gain) for small signals. Static signals are defined by the designer. The origin of small signals is usually external.