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Bucknell ELEC 350 - Diode-Based Attenuator

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IntroductionExperimental ProcedureELEC 350L Electronics I Laboratory Fall 2011Lab #8: Diode-Based Attenuator IntroductionThe piecewise linear model of the pn-junction diode under forward bias conditions includes a resistor in series with an independent voltage source. The value of the series resistance depends on the diode current, a property that can be exploited to design a remotely controlled attenuator circuit. Attenuation is a reduction in signal strength. It can be undesirable, as in the case of long distance radio communication, or it can be introduced on purpose to protect sensitive equipment from strong signals or to implement a volume control, among other uses. In this lab exercise you will design and test a simple attenuator and use it to control the amplitude of a sinusoidal signal.Theoretical BackgroundRecall that the i-v characteristic of a pn-junction diode is described by the diode equation, 1/TDnVvSDeIi,where iD is the diode current flowing in the direction of the arrow in the circuit symbol, and vD is the diode voltage, which obeys the passive sign convention (i.e., iD flows into the positive side ofvD). The constant IS is the saturation current, and the constant n is the emission coefficient, the value of which varies between one and two for most silicon diodes. The constant VT is the thermal voltage, given by600,11TqkTVT,where T is the temperature in Kelvin; k is Boltzmann’s constant (1.38 × 1023 J/K); and q is the charge on a single proton (1.60 × 1019 C). At a temperature of approximately 293 K (20 C or 68 F), VT = 25 mV.As we have seen, it can be difficult to solve circuit problems using the diode equation because of its nonlinear form. The piecewise linear (PWL) model of the diode has therefore been developed to approximate the i-v characteristic. Its circuit representation consists of linear circuit elements, specifically, an independent voltage source VF in series with a resistor rd. The i-v characteristic that corresponds to the PWL model is shown as a dashed line in Figure 1, and the actual i-v characteristic represented by the diode equation is shown as a solid curve. The accuracy of the model depends on evaluating the slope of the curve near the operating point of the diode, the partof the curve associated with the expected current through (or voltage across) the diode during normal operation. The reciprocal of the slope is equal to the value of the “on” resistance rd. If the diode current fluctuates significantly, it might be pointless to determine the value of rd since it too would fluctuate. However, in the case where the current varies little around an average value, the inclusion of rd in the diode model can be very helpful. As we shall see, it is central to the design of diode-based attenuators.1 of 5Figure 1. Piecewise linear (PWL) representation of the i-v characteristic of a pn-junction diode. The PWL representation can be modeled as an independent voltage source of value VF (which represents the diode’s turn-on voltage) in series with a resistor of value rd.Many types of attenuator circuits use internal resistances of one or more diodes as elements of a voltage divider (or more sophisticated voltage reduction circuits). A simple approach is illustrated in Figure 2. Resistor RB is chosen to establish a “quiescent,” or average, DC current flowing through the diode. The time-varying signal coming from the function generator is assumed to be weak enough so that the current it causes to flow through the diode is a tiny percentage of the DC current. Thus, the diode’s “on” resistance rd is not significantly affected by the signal current.Figure 2. A simple diode-based attenuator. Resistor RB sets the DC component of the diode current, which in turn controls the diode’s “on” resistance rd. If RL >> rd and RB >> rd, then the effect of those two resistors can be ignored, and the on resistance can be assumed to form a voltage divider with the function generator’s output resistance Rg.slope = 1/rdiDvDVFiDRLFunctionGeneratorCVS+−+vD−RgvgCRB+vo−C2 of 5The two capacitors connected to the anode of the diode in Figure 2 are called DC blocking capacitors, and their purpose is to keep DC current from flowing anywhere but through the diode. If they have large enough values, they will pass AC signals easily. Recall that the reactance of a capacitor can be determined viaCfXC21.The value of C is chosen so that the reactance is insignificant compared to Rg and rd at the lowestfrequency of interest (where XC is greatest in magnitude). The capacitor in parallel with the power supply VS ensures that any signal energy that gets past resistor RB is shunted to ground in the vicinity of the circuit rather than flowing through the power supply circuitry. It is called a bypass capacitor.The relationship between the diode on resistance and the DC quiescent current is determined by taking the derivate with respect to vD of the diode equation for the special case when vD is large enough to satisfy the approximationTDnVvSDeIi/.The derivative is TDTDnVvSTnVvTSDDeInVenVIdvdi//11.Note that the second quantity in parentheses on the right-hand side is the diode current. Thus,TDDDnVidvdi.Recall that the slope of the curve is equal to the reciprocal of the diode’s on resistance rd. Furthermore, if the AC variation around the DC quiescent level of the current is small, then we can make the approximation iD ≈ ID, where upper-case variables are used here to represent constant quantities (like DC currents), and lower-case variables represent time-varying quantities. By the way, this lower-case/upper-case convention is widely used in textbooks and technical papers. Making these two substitutions yieldsDTdInVr .The thermal voltage VT is well defined (if the temperature is known), but n is an empirically derived quantity. The value of n might be available on a datasheet, but more typically it must be determined by measurement.A circuit representation of the attenuator that is valid for AC signals only is shown in Figure 3. Note that resistor RB is depicted as grounded on one side. This is because of the bypass capacitor in the actual circuit; it shorts one side of RB to ground with respect to AC signals. Also note that 3 of 5the turn-on voltage VF of the diode is not included because it is a DC independent source. It has no effect on the AC


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