ECE 304: Diode Capacitances

Transcription

1 ECE 304: Diode Capacitances Diode (see S&S pp for I-V behavior and pp for capacitances) The small-signal equivalent circuit for a semiconductor diode is shown in Figure 1. Its components are discussed below. r D C J C T FIGURE 1 Small signal circuit for a semiconductor diode: a parallel combination of diode resistance r D, junction capacitance C J and transit time capacitance C T COMPONENTS DIODE RESISTANCE r D The resistance r D is related to the slope of the diode I-V curve at the Q-point, as diagrammed in Figure 2. ι D 1 r D ι = D υd Q I DQ V DQ υ D FIGURE 2 Diode I-V curve showing how diode resistance is related to the slope at the Q-point From Figure 2 it is clear that the diode resistance changes when the Q-point changes. Using the diode law of EQ. 1 υ D = nvth ι D IS e, where I S is the diode scale current or what is called the saturation current in PSPICE, n = ideality factor, or what is called the emission coefficient in PSPICE, we find EQ. 2 υ r D nvth D = = = ιd ιd Q po int nvth I DQ JUNCTION CAPACITANCE The junction capacitance C J is very much like an ordinary capacitor. It is determined by the spacing between the positive charge on the p-side of the junction and the negative charge on the n-side as C J = Area κε 0 / W, where Area= junction area, κ = 11.7 = silicon dielectric constant, ε 0 = permittivity of empty space (8.85 x F/cm 2 ) and W = separation of positive plate from negative plate. However, a difference from ordinary capacitors is that the plate separation W changes as the voltage across the junction changes: the larger the reverse bias voltage, the Unpublished work 2004 John R Brews Page 1 2/12/2005

2 bigger W becomes because reverse bias pulls the positive charges and negative charges apart. On the other hand, forward bias increases C J by pushing the charges together. PSpice includes these changes in C J with bias, but in hand calculations we ignore it. DIFFUSION OR TRANSIT TIME CAPACITANCE The diffusion capacitance, or what PSPICE calls the transit time capacitance C T is a different kind of capacitance, related to charge that is stored in the diode when it is forward biased. Forward bias of the diode causes the diode to conduct current I DQ at the Q-point. This current implies a certain amount of charge is transported through the diode per unit time. That is, I DQ = Q DQ /τ T where Q DQ is the charge inside the junction and τ T is the time it takes this charge to cross the diode (called the storage or transit time). If we change the diode voltage drop, this charge Q DQ will change to the value required at the new Q-point. This change in stored charge with diode voltage is the diffusion capacitance, i.e. EQ. 3 C T = Q DQ / υ D = I DQ τ T / υ D = I DQ τ T /(nv TH ) where V TH = thermal voltage Thus we see that the diffusion capacitance C T = I DQ τ T /(nv TH ) depends on the current at the Q-point. In practice this means that to predict the RC time constants, and hence the frequency response of our circuits, we must take into account the change in C T with the choice of I DQ at the bias point. Diode Capacitance (F) IMG(1/V(OUT_I))/(2*pi* ) Formula 1.E-07 1.E-08 1.E-09 1.E-10 1.E-11 1.E-12 1.E-10 1.E-09 1.E-08 1.E-07 1.E-06 1.E-05 1.E-04 1.E-03 1.E-02 Diode Current (A) FIGURE 3 Diode capacitance from PSPICE compared with formula of EQ. 3 Figure 3 shows the PSPICE result for the ideal diode of Figure 6 below. Notice that the currentindependent junction capacitance dominates out to about 0.1 µa, and then the transit-time capacitance takes over, causing a linear increase in capacitance with Q-point current. The junction capacitance for the formula used in Figure 3 was C J from the diode dot-model statement, which is a little different from the PSPICE value, which includes the bias dependence of the junction capacitance. Summary: The pn-diode exhibits two types of capacitance: junction capacitance, which depends on voltage, and diffusion capacitance, which appears only under forward bias and depends on current and storage time. Examples and Exercises EXAMPLE 1 Use PSPICE to find the corner frequency for the circuit of Figure 4. Unpublished work 2004 John R Brews Page 2 2/12/2005

3 Sweep uA mV PARAMETERS: DOT-MODEL R1 OUT_V IS = 1pA VA = 1V {R} CJ = 3pF R = 1k TT = 400ns uA Ideality = 2 V1 D1 - {VA} PROBE OUTPUT FILE Diode NAME D_D1 V2 MODEL Diode AC 1V ID 6.75E-05 - VD 9.33E-01 0 REQ 7.67E02 CAP 5.28E-10.model Diode D Is={IS} Cjo={CJ} Tt={TT} N={Ideality}) FIGURE 4 Schematic for voltage-in, voltage-out circuit; dot-model statement for diode at top; OUTPUT FILE data for Q-point at right Solution: We run a small-signal AC sweep simulation profile to obtain the results of Figure 5; the line is added that shows a value equal to the maximum gain divided by 2 (3 db point). 500mV ( K, m) 250mV ( , m) V(OUT_V) FIGURE 5 Determination of corner frequency of voltage gain as 693 khz EXAMPLE 2 Use PSPICE to find the corner frequency for the circuit of Figure 6. AC Sweep.model Diode D Is={IS} Cjo={CJ} Tt={TT} N={Ideality}) I1 I uA R2 {R} mV D2 Diode OUT_I uA PARAMETERS: VA = 1V R = 1k PARAMETERS: I_D = 1m DOT-MODEL IS = 1pA CJ = 3pF TT = 400ns Ideality = 2 PROBE OUTPUT FILE 1A {I_D} NAME D_D1 MODEL Diode 0A mA ID 6.75E-05 VD 9.33E-01 0 REQ 7.67E02 CAP 5.28E-10 FIGURE 6 Alternative circuit for current-in, current-out Solution: We run a small-signal AC sweep simulation profile to obtain the results of Figure 8; the frequency where the gain increases by 3 db is labeled. Unpublished work 2004 John R Brews Page 3 2/12/2005

4 50 25 ( , ) ( K, ) V(OUT_I) FIGURE 7 Transresistance gain for circuit of Figure 6; 3dB corner is marked 1.00A ( G, ) 0.75A ( , m) ( K, m) ( K, m) 0.50A I(D2) FIGURE 8 Diode current vs. frequency for Figure 6; frequencies 1/(2πCr) and 1/[2πC(r//R)] are marked EXAMPLE 3 Derive the results of Example 1 using hand analysis and the equivalent circuit of Figure 1. EXAMPLE 4 Derive the results of Example 2 using hand analysis and the equivalent circuit of Figure 1. EXAMPLE 5 Verify your PSPICE results for Examples 3 and 4 by comparison with your hand analysis in a spreadsheet EXAMPLE 6 Generate Figure 3 EXAMPLE 7 Use PSPICE to plot the corner frequency as a function of the Q-point current for Figure 6. Explain why the one plot shows a downward step as a function of I D, while the other shows a steady rise until it saturates. Unpublished work 2004 John R Brews Page 4 2/12/2005

5 100M ( u, M) ( u, M) ( m, K) ( m, K) 100K 10u 100u 1.0m 10m 100m upper3db(v(out_i)) I_D FIGURE 9 Example corner frequency plot vs. DC input current for transresistance gain made using PROBE (Figure 6, voltage output); R=1 kω fc (Hz) 1.E08 1.E07 1.E06 Formula PSpice 1.E I(uA) FIGURE 10 Comparison of formula with PSPICE for case in Figure 9; see note below 1 100K ( p, ) ( m, K) ( u, K) 10 10p 100p 10n 1.0u 100u 10m upper3db(v(out_i)) I_D FIGURE 11 Example corner frequency plot vs. DC diode current for transresistance gain made using PROBE (Figure 6, voltage output); R=1 TΩ 100m Reference 1. See the on-line PSPICE Reference Guide C:\Program Files\OrcadLite\Document\PSpcRef.pdf if you have a standard installation of Orcad Lite pp S&S pp for diode I-V behavior and pp for diode capacitances 1 Notice that in Figure 6 the applied DC current I_D is not the diode Q-point current unless R=. To use formulas, we need the diode current. One way to do this is to use PSPICE to determine a plot of diode current vs. I_D and use this curve in the spreadsheet to relate calculated bandwidth to the current I_D. Unpublished work 2004 John R Brews Page 5 2/12/2005