Circuit : Half-Wave Rectifier /2 Wave Rectifier Behavior R (ideal) (.7V drop).5.5 2 2.5 3 The /2-wave rectifier circuit passes current only when >.7V. In this case, the diode s forward voltage drop is close to.7v, regardless of the current that flows, so that.7v. When the diode is OFF, no current flows, so V. Hence we can describe the circuit s behavior as max (,.7V). Detailed Examples Case A: < In this example, let = V and R = kω. We want to solve for. First, we assume the diode is OFF and check for consistency. We find that = and therefore the diode s forward drop is v D = V. Since v D is negative, the diode must be OFF, so = V. Case B: = V In this case the diode is clearly ON. Using the constant voltage drop approximation, we can estimate that.3v. A more precise estimate may be obtained using the small-signal model: ma 26 Ω +.7V kω
+.7V + kω ma = ( 26 + ) = ma +.7 kω 26 = (ma) ( kω) +.7 26 ( kω) Now notice that (26 ) 26 (try it). Then we can simplify the approximation: 26mV +.7V.684V. This provides a more accurate approximation when the resistor R is large. In the case where = V, we find that Circuit 2: Regulator.343V i D 343µA The regulator circuit is similar to the /2-wave rectifier, only it interchanges the positions of the diode and resistor:.7v Regulator Behavior.5.5 2 2.5 3 In this circuit, when <.7V, the diode is either OFF or only weakly ON, so the current is close to zero. In that case, the voltage drop across R is nearly zero, so. When >.7V, the diode is clearly ON. Using the constant voltage drop model, we find that.7v, so the waveform is clipped at.7v. A more accurate analysis is obtained using the small-signal model: 2
R ma.7v + By applying the node-voltage method at, we find that R +.7V ( R + ) + ma = = R +.7V = + R +.7V R R + As the name implies, regulators are used to produce stable DC voltages. Ideally, a regulator should produce.7v regardless of (so long as >.7V). The preceding analysis revealed a slight dependency between and : ( ) =. R + In practice, the residual signal can introduce interference into the circuits that are interfaced with the regulator. According to this analysis, the regulation works best when R is large. Circuit 3: Peak Rectifier The peak rectifier (or peak detector) circuit is like a rectifier that uses a capacitor in place of the resistor. This circuit can be interpreted as an integrating rectifier. C Unlike the usual diode circuits, the.7v approximation can be misleading when applied to the peak rectifier. This is because the capacitor integrates all of the current that passes through it: = C tf i D (t) dt. 3
When the diode is OFF, a small current still flows, and that current is steadily accumulated by the capacitor s integrating behavior. Consider the output from a SPICE simulation where C = nf, shown below. In this simulation, we can see that rises initially to.263v, which is approximately.437v. Clearly the.7v model is not working. Peak Detector Circuit with.7v Input Amplitude.8.6.4.2.2.4.6.8..2.3.4.5 To understand why the.7v model fails, we may examine the diode current, shown in the figure below. Although the current never exceeds µa, the small pulses are sufficient to charge C. 3 8 Peak Detector Current i 2.5 Current 2.5.5..2.3.4.5 In each cycle of the input waveform, the peak current gets smaller, so the output waveform marches in smaller and smaller steps toward the peak value of the input voltage. Given enough time, will eventually rise very close to the actual peak. This effect can be used to create AC-to-DC converters. 4
The peak detector circuit can also be used in a variety of applications for instrumentation and communication. In these applications, we usually want to detect the envelope of some waveform, which requires that be allow to drop when decreases. This is accomplished by adding a resistor R in parallel with C, resulting in an envelope detector: C R An example SPICE simulation result is shown in the plot below. This simulation used the following values: C = µf R = kω f = Hz In this circuit, the diode is able to rapidly charge the capacitor C, which is then slowly discharged by R. Envelope Detector 4 2 2.2.4.6.8.2.4.6 When the didoe is OFF, the output waveform is described by the standard RC discharge equation (t) = v peak ( exp ( RC (t t ))), where t is the time when the diode turns OFF. 5
SPICE simulation example for the envelope detector circuit: envelope d e t e c t o r c i r c u i t Generic diode model :. model diode d ( I s =2.298 e 5, n=) The input i s a damped Hz s i n e wave that l o o k s l i k e an impulse : Vin SIN ( 5.25 8) Peak d e t e c t o r c i r c u i t : D 2 diode C 2 uf R 2 k Transient s i m u l a t i o n :. tran m. 5. end 6