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1. Overview A resistor is a two-leads radio component designed to oppose an electric current by producing a voltage drop between its terminals in proportion to the current, that is, in accordance with Ohm's law: V = IR. The resistance R is equal to the voltage drop V across the resistor divided by the current I through the resistor. The primary characteristics of the resistor is its resistance and the power it can dissipate. Other characteristics include temperature coefficient, noise, and inductance. Practical resistors can be made of resistive wire, and various compounds and films, and they can be integrated into hybrid and printed circuits. Size, and position of leads are relevant to equipment designers; resistors must be physically large enough not to overheat when dissipating their power. Variable resistors, adjustable by changing the position of a tapping on the resistive element, and resistors with a movable tap ("potentiometers"), either adjustable by the user of equipment or contained within, are also used. Resistors are used as part of electrical networks and electronic circuits. There are special types of resistor whose resistance varies with various quantities, most of which have names, and articles, of their own: the resistance of thermistors varies greatly with temperature, whether external or due to dissipation, so they can be used for temperature or current sensing; metal oxide varistors drop to a very low resistance when a high voltage is applied, making them suitable for over-voltage protection; the resistance of a strain gauge varies with mechanical load; the resistance of photoresistors varies with illumination; the resistance of a Quantum Tunnelling Composite can vary by a factor of 1012 with mechanical pressure applied; and so on.This schematic has two astable states. In state 1 transistor T2 is conducting and transistor T1 is non-conducting. The feedback between the two transistors is achieved using capacitors C1 and C2. The time period for each state can be adjusted. 2. Analysis Before starting the circuit (no voltage applied) both capacitors C1 and C2 are charged with 0V. Upon applying voltage to the circuit, even if the schematic is symmetrical, due to assymetry caused by unideal conditions, one of the transistors will conduct greater current than the other. Let's assume this is T2 that will conduct more current than T1. Thus the voltage over resistor R4 will be higher than the voltage over resistor R1. This will result to driving the base voltage of T1 to a lower value than the base voltage of T2. This T1 will become less conductive than T2. This process represents a positive feedback that will lead to immidiate switching of the schematic to state 1. T1, being blocked, will let C1 charge itself to the supply voltage minus the base-emitter on voltage of transistor T2 and minus the forward voltage of diode D2: (1.)
C2 will charge negatively to: (2.) VC2 = VCE(sat)-T2 - ( VBE(on)-T1 + VF-D1 )Here VCE(sat)-T2 is the collector-emitter saturation voltage of the conducting T2, VBE(on)-T1 is the base-emitter on voltage of T1 and VF-D1 is the forward voltage of D1. Once in state 1 the circuit will charge the capacitors C1 and C2 as specified. The transition to state 2 will occur when the charging of C2 completes and the base-emitter current of T1 increases. This increase will raise the voltage over R1 thus pushing the base voltage of T2 through C1 down. T2 will decrease its conductance and the voltage over R4 will raise. This will increase the base voltage of T1 and the process will result in positive feedback which will switch the circuit to conduncting T1 and non-conducting T2. During state 2 the capacitors charging will take the reverse path. In each state of the circuit, one of the capacitors is charging through the collector (R1 or R4) and the other capacitor is discharging through the base resistor (R3 or R2). The switching occurs when the capacitor charging throught the base resistor get charged. So this charging process should take longer, i.e. the base resistor should be greater than the collector resistor:
(3.) R2 > R4
There is another condition for the resistors and it comes from the current amplification of each transistor, which is also called the dynamic forward current transfer ratio in common emitter circuit - h21e. R2 and R3 should conform to: (5.) R2 < R1 * 0.5 * h21e-T1(6.) R3 < R4 * 0.5 * h21e-T2 Where 0.5 is a security factor. Finally, D1 and D2 are used to protect the base-emitter junctions of T1 and T2 from reverse voltage higher than the emitter-base maximum voltage of the used transistors. Normally, this voltage is around -5V for silicon NPN transistors. D1 and D2 are used when the power supply is higher than 5V. C3 and C4 are blocking (filtering) capacitors. The charging effect of the capacitor through the collector resistor delivers non-rectangular output voltage from the schematic (see fig.1). To obtain uniform rectangular output (fig.2) a variation of the schematic is shown below. The period T of the periodic process can be approximately calculated with the following equation: (7.) T = 0.7 * R2 * C2 + 0.7 * R3 * C1Here 0.7 * R2 * C2 is the time constant of state 1 of the circuit and 0.7 * R3 * C1 - of state 2 respectively. The two output voltage levels V1 and V2 are determined as follows:
(8.) V1 = VCC Equation (8.) is valid if we assume that the leackage currents ICEO-T2, IL-C2 and IR-D3are neglected. VCE(sat)-T2 is the collector-emitter saturation voltage of T2. 3. Synthesis The synthesis of the circuit generally starts with the selection of R1 and R4 resistors according to the needs of power load. Then the base resistors are selected using (5.) and (6.), but not to violate (3.) and (4.). After this step, the periods of state 1 and state 2 are chosen. Finally, the capacitance of C1 and C2 is calculated using (7.). A sample printed circuit board layout (PCB layout) is shown below. |