Microelectronic Circuits Study Guide (Chapter 4)

Chapter 4: Diodes Some circuit devices exhibit nonlinear characteristics, but can be used in linear electronics - diodes are two-terminal devices that exhibit nonlinear i − v characteristics - diodes are useful for many purposes, such as rectification and amplification - several models can be used to represent the diode at varying levels of accuracy and complexity 4.1: The Ideal Diode Diodes typically have a positively charged terminal (an anode) and a negatively charged terminal (a cathode) - an ideal diode simply has two modes: when a positive voltage is applied over the anode and cathode (“forward-biased”), the diode behaves as a short circuit; no voltage is absorbed, and current passes through freely (the diode is “on”) - when a negative voltage is applied over the anode and cathode (“reverse-biased”), the diode absorbs all voltage, and passes no current (the diode is “off ”) - the i − v characteristic of this device is piecewise linear: a horizontal zero-current section at v ≤ 0, and a vertical section at v = 0+ Rectification: Ideal diodes can be used as a rectifier circuit, which converts a bidirectional alternating signal into a unidirectional signal - the input signal vi has an average value of zero, and the output vo has a positive average value (which can be considered a “DC component” over which the output signal alternates) Diode logic gates: A combination of diodes can function as a logic gate when provided with discrete input voltages (such as 0 volts representing a “low” value and +5 volts representing a “high” value) - a logic OR and AND gates can be formed this way: 17 4.2: Terminal Characteristics of Junction Diodes Simple diodes can be formed from a pn junction, which conducts substantial current in the forward direction and almost no current in reverse - the typical pn junction exhibits a positive vertical current at a small positive voltage −VZK ; a negative vertical current at a certain large negative voltage; and a zero current at intermediate voltages (the “breakdown” region): In a more accurate representation, the zero-voltage reverse-biased region exhibits a small leakage current, and the transition points represent nonlinear, exponential growth over a small voltage range: 18 The forward-bias region exhibits current according to the equation: v i = IS (e VT − 1) IS = saturation current (specific to a particular diode, and temperature-sensitive) v = input voltage VT = thermal voltage = kT q J = 1.38 · 10−23 K k = Boltzmann’s constant = 8.62 · 10−5 eV K T = temperature in kelvin q = electron charge = 1.6 · 10−19 C Alternatively, VT = 0.0862T mV; at room temperature, VT = 25.3 mV Saturation current scales proportionally with the cross-sectional area of the diode: if the diode cross-section doubles, IS doubles - saturation current is also very temperature-sensitive: at T + = 5◦ , IS doubles - however, IS is typically in the range of 10v−12 for silicon diodes, so for any significant amount of forward current, i ≈ IS e VT Diode voltage can also be expressed as v = VT ln Ii - a ratio of voltages and S currents can be expressed as V2 − V1 = VT ln II12 In practice, forward current is typically negligible for any positive voltage up to about 0.5 V (the “cut-in voltage”), and then turns almost vertically positive therefore, when a pn junction diode is “on” with any forward voltage exceeding the cut-in voltage, the diode absorbs a constant voltage (about 0.5 V) and otherwise operates as a short - diodes typically have a current rating indicating a range of forward currents over which the diode functions as expected 19 Since IS is temperature-sensitive, the voltage drop is also temperature-sensitive: Reverse-biased region: The current in this region is largely determined by the saturation current: i ≈ IS - actual diodes typically exhibit a somewhat larger reverse current (e.g., 1 nA) due to leakage effects, which are also temperaturedependent and tend to double for T + = 10◦ Breakdown region: When the reverse voltage exceeds a threshold value ( VZK ), voltage increases steeply - the diode is not destroyed in this process, but the abrupt change in the neighborhood of VZK may cause current to change rapidly over a small fluctuation in voltage 4.3: Modeling the Diode Forward Characteristics Exponential model: The most accurate description of the forward characteristic VD is the exponential model presented above, where ID = IS e VT when VDD ≥ 0.5 V - when the diode is included in a circuit featuring a resistor, the current can also be modeled according to Kirchhoff’s current law: ID = VDDR−VD Graphical analysis: The Kirchhoff’s current law equation provides a line in the v − i plot with slope − R1 (the “load line”) - the exponential model provides a non-linear equation for the current through the diode - the intersection of these equations provides an intersection point (the “operating point”) indicating the actual voltage and current of the diode 20 Iterative analysis: The equations above can be applied iteratively until the values converge Example: For a diode that exhibits 1 mA at a voltage of 0.7 V, find the current ID and voltage VD when positioned in a circuit with VDD = 5 V and R = 1 k Ω. Answer: Start with the load line equation, ID = VDDR−VD : −0.7 ID = 51000 = 4.3mA Next apply the exponential equation, V2 − V1 = VT ln II12 = 25mV ln II21 : )) = 0.738 V V2 = 0.7 + (25mV · ln( 4.3mA 1mA Apply the load line equation again: 5−0.738 ID = 1000 = 4.262mA Apply the exponential equation again: V2 = 0.738 + (25mV · ln( 4.262mA )) = 0.738 V 4.3mA This yields convergence at ID = 4.262mA, V2 = 0.738V, which is our answer Constant-voltage-drop model: A less accurate but easier estimate of diode behavior can just presume that the diode imposes a constant voltage drop on a forward voltage: 21 Ideal-diode model: Completely neglecting the voltage drop enables very quick analysis, but exhibits significant inaccuracy; the constant-voltage-drop model is almost as conceptually easy and provides a much better approximation Small-signal model: In some cases, a small alternating signal vd (t) is imposed on a large DC voltage VD - we can find the slope of the exponential curve at the quiescent point VD , and then presume that over this small range, curve is relatively linear - the linearity is estimated according to the incremental resistance rd = IVDT = VTVD - this small-signal approximation works when |vd (t)| ≤ 0.5mV IS e V T Voltage regulation: Diodes are used to create a regulated voltage, where a circuit provides a constant DC voltage in spite of changes in the load and/or changes in the power supply voltage - because the diode exhibits a nearly constant voltage over a large range of currents, the input to a diode will exhibit a relatively steady 0.7 V over a wide range of currents - higher voltages can be achieved by connecting diodes in series; e.g., a series of three diodes provides a steady 2 V over a wide range of currents 4.4: Operation in the Reverse Breakdown Region - Zener Diodes The abrupt change in the reverse breakdown region can be useful in some contexts, such as voltage regulators, because the diode maintains its voltage with high precision over a range of currents - zener diodes are manufactured that operate specifically in this range - a zener diode can be positioned in a reversebias position and subjected to a negative voltage from anode to cathode (i.e., a positive voltage over the cathode to anode); the diode consumes a very specific voltage ( VZ ) over a range of currents ( IZ ) - the consumed voltage does change slightly, based on an incremental resistance rz , such that δV = rz δI , but this value is typically in the range of 10 Ω - in the actual “knee” region near VZK , the resistance changes abruptly, so it is best to avoid operating a zener diode 22 in this region - zener diodes are available with VZ in the range of a few volts to hundreds of volts, and can operate within a range of currents A simple model of zener diodes is reflected by the equation VZ = VZ0 + rz IZ in practice, VZ0 is very close to VZK The zener voltage is temperature-dependent, and is defined by a temperature coefficient, TC (mV / ◦ C), which can be positive or negative - each zener diode has a particular profile curve for TC at a range of voltages; many zener diodes have a current point where TC = 0, and therefore are not temperaturedependent when operated at that current - the temperature coefficient can also be reduced by connecting a reverse-biased zener diode in series with a forwardconducting diode that has an opposite temperature coefficient 4.5: Rectifier Circuits Diodes are useful as rectifiers in many context - example: in an AC-to-DC power supply, an alternating current is provided to a full-wave diode rectifier that produces a fully rectified current, then to a low-pass filter that averages each rectified cycle (but which still exhibits a time-dependent “ripple”), and finally to a voltage regulator that provides a constant current to a load (This process often begins with a step-down transformer: a first voltage, such as 120 V, runs through a first coil with N1 turns that induces a current in a second N2 coil with N2 turns, so that the voltage fed into the diode rectifier is 120 · N 1 - in addition to stepping down the voltage, this also electrically insulates the equipment from surges on the line) Half-wave rectifier: ( 0, vs < VD - two relev s − V D , vs ≥ V D vant factors for rectifier diodes: maximum current-handling capability, and peak inverse voltage (PIV) that diode must withstand without reaching breakdown - best to use diodes where VZK is well above the PIV - rectifier diodes also do Using the constant-voltage-drop model, v0 = 23 not work well for small-voltage signals; these scenarios call for a combination of a diode and an op-amp Center-tapped full-wave rectifier: A full-wave rectifier can be designed by center-tapping the step-down coil of the transformer, and using two diodes that direct current away from either end - the average power of this rectifier will be larger than for the half-rectifier - however, each diode experiences PIV = 2Vs − VD Bridge rectifier: A bridge rectifier can be designed as a Wheatstone bridge, featuring a combination of two pairs of diodes, each of which passes current over a load resistor during half of a cycle and resists the flow of current during the other half of the cycle - bridge rectifiers use twice as many diodes as a center-tapped rectifier, and also imposes a two-diode voltage drop instead of a one-diode voltage drop - however, the bridge rectifier does not require center-tapping, and therefore required a coil that is half the length of the center-tapped rectifier - also, the PIV is distributed over two diodes, as PIV = Vs − VD Peak rectifier: 24 (Note: This is a half-wave peak rectifier; a full-wave peak rectifier can be constructed by also including a diode across the load resistor) - in order to transform an AC rectified voltage into a DC voltage, a capacitor can be added in parallel with the load resistor - the capacitor rapidly charges when the voltage is near its peak, and then discharges to maintain the voltage while the rectified current falls - as the capacitor discharges, it loses a bit of voltage until the next peak of the source voltage - the result is a nearly-DC voltage with a “ripple” as the capacitor charges and discharges, which is determined as: Vo = Vp − 21 Vr , where Vp = peak voltage Vr = ripple voltage magnitude, where IL Vr = fC The conduction interval δt is defined as: Vp cos(ωδt ) = Vp − Vr Peak rectifiers can be used as peak detectors, such as an AM demodulation devices Precision half-wave rectifier: A “superdiode” can be generated with the addition of an op-amp to provide a half-wave rectified output v0 that captures the full amplitude of the input signal - this occurs because the feedback loop causes the op-amp to drive an output voltage of va = vi + vD , i.e., higher than the input voltage - the actual output voltage, after the diode voltage drop, is vo = va − VD = vi 25 4.6: Limiting and Clamping Circuits Voltage limiter: Since diodes provide a (nearly) constant voltage drop in a forward-biased range, diodes can be used to impose as a voltage limit - the constant-voltage-drop model causes this to appear as a “hard limit” with a sharp inflection point, but real diodes provide a “soft limit” with a more gradual approach to the cutoff voltage - limiting can be imposed on positive or negative voltage (by reversing the orientation of the diode), and can be offset by placing a voltage source in series with the other side of the diode - two limits can be imposed with a pair of diodes Clamped capacitor: When this voltage source provides a negative voltage of −V , current flows through the diode (which has zero output) until the capacitor is fully charged when the voltage source then shifts to a positive voltage +V , the diode resists the flow of current, with a magnitude of +V − (−V ) - the result is that where the input voltage varies from −V to +V , the diode exhibits an output voltage of 0 to (+V − (−V )) - that is, this diode adds a DC component to the fluctuating AC source; the output is said to be “clamped” at a higher value - adding a resistor in parallel with the diode allows current to flow during each cycle, causing a slightly skewed output Voltage doubler: 26 The combination of a clamped capacitor and a peak rectifier causes an output that is twice the magnitude of the input 4.7: Special Diode Types Schottky-Barrier Diode (SBD): This type of diode is not formed by a pn junction, but by an n-type material in contact with metal - while operating very similarly to a diode, this diode does not exhibit capacitance in the n-type material, thus avoiding capacitance and raising the switching speed of the diode the forward voltage drop is also lower (0.3 to 0.5 V, vs. 0.6 to 0.8 V) Varactors: The reverse-bias capacitance of the depletion region is voltagedependent, and can be used in some applications (e.g., self-tuning radio receivers) - special diodes called varactors can be designed that exhibit this property with consistent voltage-dependent variance Photodiodes: Most diodes are shielded from light, because photons can break covalent bonds in the depletion and create a current - optoelectronics can make use of this effect by exposing the junction to light that increases the current of a set voltage when exposed to light - solar cells also make use of this effect to transform light into voltage Light-emitting diodes: A diode made with a particular type of material (directbandgap material) causes light to be emitted when carrier-injected minority carriers recombine with majority carriers in each region - LEDs can be made to produce light across a variety of wavelengths, including single-wavelength LEDs (“laser diodes”) Optoisolator: An LED can transform voltage into light that is then captured by a photodiode and converted back into voltage - this combination enables the transmission of voltage with electrical isolation, which reduces interference and the effects of current surges and spikes 27