Analysis and Design of Electronic Circuits: Chapter 3 - Diodes, Study notes of Electrical and Electronics Engineering

Download Analysis and Design of Electronic Circuits: Chapter 3 - Diodes and more Study notes Electrical and Electronics Engineering in PDF only on Docsity! Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diode 1 Chapter 3: Diodes This lecture covers Section 3.1-3.3 1. Ideal diode: I-V characteristics 2. Rectifier and logic gates 3. Terminal characteristics 4. Diode models Notes: A few words about diodes: • Diode is one of the most commonly used electronic elements in micro-electronic circuits. • As the simplest and most fundamental nonlinear circuit element, diode can perform many signal-processing functions that can not be performed by linear circuit such as ideal op-amp. • Knowledge of diode is a must to further our studies on three- terminal elements such as transitors, MOSFET. Ideal diodes The ideal diode can be modeled as the following: • If a –voltage applied, then the diode is reverse biased, no current flows, diode behaves like an open circuit. • If a +voltage applied, then the diode is forward biased, large current flows with ZERO voltage drop, diode behaves like a closed circuit. To prevent large forward current, current- limiting resistors are often used to reduce the forward current. • This simplest nonlinear response is referred as piece-wise linear. Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diode 2 Application I: rectifier Application II: Diode logic gates CBAY ++= CBAY ⋅⋅= Terminal characteristics of junction diodes: Almost all diodes used today are made of semiconductors (i.e. Si). When Si with different dopants were brought together, a “pn-junction” was formed. The actual characteristics of diodes were determined by the pn-junction. In a “real” diode, the I-V curve consists of three distinct regions: • The forward-bias region (v>0) • The reverse-bias region (v<0) • The breakdown region (v<-VZK) The Forward-Bias Region: In the forward region, the i-v follows exponential function closely: ( ) q kTVeIvi T nV v S T = ⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ −= 1 In the above formula • IS: saturation current (T-dependant, ~10-15A, double every 5oC) • VT: thermal voltage (~25 mV @ 20oC) • k=1.38×10-23 J/K (Boltzmann’s constant) • T=273+ Celsius: the absolute temperature • q=1.60×10-19 coulomb: charge carried by single electron • n: material dependant constant (n~1-2, for IC n~1). Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diode 5 The Small-Signal Model: In many applications, the diode is biased at an operational point (bias point) on the forward i-v curve. Then a small ac signal is superimposed on that. This scenario is shown below. Of course, we are mostly interested in the characteristic of ac signal when passing the diode, this is so-called small-signal model. To handle this situation, we first determine the voltage VD and the current ID of the bias point, then we linearize the i-v curve of the diode around the bias point. Therefore, the I-V curve around bias point will be a straight line and characterized by the small signal resistance: D T IiD D d I nV v i r DD =⎥ ⎦ ⎤ ⎢ ⎣ ⎡ ∂ ∂ = = 1 The i-v relationship of the small ac signal can be described using small-signal approximation: d T D d vnV I i = Let’s derive these relationships in class: Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diode 6 Example: Consider the voltage-regulator circuit shown below. The value of R is selected to obtain an output voltage VO of 0.7 V. a). Use the small signal model to show that the change in output voltage corresponding to a change of 1V in V+ is 7.0−+ = Δ Δ ++ T TO nVV nV V V (mV/V) b). Generalize the expression above for the case of m diodes connected in series and the value of R adjusted so that the voltage across each diode is 0.7 V (and VO=0.7 mV). Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diodes 1 Chapter 3: Diodes This lecture covers Section 3.4-3.6 1. Zener diodes 2. Half-wave and full-wave rectifiers 3. Peak rectifier 4. Super diode 5. Limiting and clamping circuits Notes: In this lecture, we study some of most commonly used circuits involving diodes. All these circuits make use of either forward or backward nonlinear characteristics. Zener Diodes In the reverse bias, when the reverse bias voltage goes beyond the breakdown voltage –VZK, we observe rapidly increase of current as shown below: When the diode is used to operate at the breakdown region, we refer it as Zener diode. Since the slope is extremely large, a large current change across the Zener diode will only lead to very small voltage change. Therefore, Zener is mostly used as a voltage regulator. The exact I-V curve for Zener is very complicate, however, we can implement piecewise-linear model, and use the incremental resistance rz and breakdown voltage VZ0 as the following: ZzZZ IrVV += 0 The model is shown above. Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diodes 4 The Bridge Rectifier Another popular used full-wave rectifier is shown below and known as the bridge rectifier. The peak inverse voltage Ds VVPIV −= While VS and VD are the maximum or amplitudes of sinusoid signal. Here is the analysis: • Positive cycle, the total reverse voltage applied to D3 )()( 23 forwardvvreversev DOD += • Negative cycle, the same • So, the vO is )(2 forwardvvv DSO −= Therefore, the PIV is shown above. The Rectifier with a Filter Capacitor Above rectifiers produce DC output with too much voltage variation. This variation can be substantially reduced by adding a capacitor. Let’s first consider an open-circuit scenario, which illustrate how a capacitor can level off the voltage variation. Now, if we add a load to the circuit shown below, the voltage output won’t be perfect leveled as shown. Now, let’s analyze this circuits by assuming the time-constant of RC>>T, where T is the period of the input sinusoid. Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diodes 5 Summary: • The peak-to-peak ripple voltage: RC TVV Pr = • Conduction interval: pr VVt /2≈Δω • Average charging current: ( )rpLDav VVIi /21 π+= • Peak charging current: ( )rpLD VVIi /221max π+= The precision half-wave rectifier or the super diode Rational: When we need super diode. • When a weak AC signal need rectification, if the peak voltage is less than 0.7 V, then diode won’t work. It needs amplification. • In an instrumentation develop, when the lost of 0.7V due to the turn-on voltage of diode is too much. In these situations, a precision half-wave rectifier circuits using an op- amp can be develop shown below. Here is explanation on • Why it can rectify less than 0.7V AC? 2). • Why turn-on voltage of diode won’t offset the output. Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diodes 6 Limiting and Clamping Circuits Since diodes will not be turned on when the voltage is below VD (~0.7V), it can be used to build limiter/clipper circuits. Figure below show the transformation functions for hard and soft limiters. We will have a few more design using diode to realize limiter circuits as shown below. The Clamped capacitor or DC Restorer By using diode, we also can design two useful circuits call DC restorer. Which provide a pulse-signal with a well-defined DC level. Here is how it works. Utilizing the similar circuits, we also can design a voltage doubler. Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diodes 3 greatly increased by doping Si with donor (electron rich) and acceptor (hole rich). • Donors such as phosphorus provides one more electron • Acceptor such as boron provides one more hole • For n-type Si, if donor concentration is ND, in thermal equilibrium, the electron concentration is close to ND Dn Nn ≈0 Where the subscript n denotes n-type, 0 denotes equilibrium. Semiconductor physics yields that the product of electron and hole concentration remains constant. D i n inn n n p npn 2 0 2 00 = =⋅ Here electron is the majority carrier, hole is minority carrier. • For p-type Si, if acceptor concentration is NA, in thermal equilibrium, the electron concentration is close to NA Ap Np ≈0 Where the subscript p denotes p-type, 0 denotes equilibrium. A i p ipp n n n npn 2 0 2 00 = =⋅ The pn-junction under open-circuit conditions: When p-type and n-type Si are brought together a pn-junction is formed shown below. • The hole in p-region diffuses into n-region, electron in n-region diffuse into p-region. • So around junction, p-region has more net negative charge, n- region has net positive charge. It forms a space-charge region or depleted region. It exists on both side of pn-junction. • These space charge region produce E-field, the E-field produces a built-in voltage: ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = 20 ln i DA T n NNVV • The space charge width in n-region and p-region are 0 112, V NNq xxW N N x x DA s pndep D A p n ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ +=+== ε Typically, Wdep around 0.1-1 μm. • The potential field serves as barrier so majority carrier (hole in p-side and electron in n-side) has to overcome to get into the other side. Thus, diffusion current ID depends on Vo. • So now we have built-in E-field, but how does it stop diffusion current??? Well, don’t forget we still have electron (minority) in p- region, although it is much less than holes. When electron randomly gets into space-charge region, E-field will quickly swift it to n-region by drifting! This process occur in n-region too (this time is for holes). Therefore, a dynamic balance is established! Diffusion current is equal to drift current. DS II = Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diodes 4 The pn-junction under reverse-bias conditions: If the pn-junction is reversely biased, then: • Space charge region becomes wide, built-in field get stronger. • It will be more difficult to for majority carrier to diffuse through, therefore ID drops! • The drift current IS will remain relatively as constant since it only depends on E-field strength not voltage! Therefore, it will lead to a constant reverse current in steady state! DS III −= This is where the reverse current of diode comes from. The depletion capacitance In additional of reverse biased current, as the voltage across the pn- junction changes, the width of the depletion region changes, so as the total charge stored in. This behaves like a capacitor. To find the capacitance, we like to find out the total charge qJ (either positive or negative) stored in the junction. ( )R DA s dep dep DA DA nDJ VV NNq W AW NN NN qAxqNq +⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ +⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ = + == 0 112ε As we can see, the charge qJ vs. VR is a nonlinear relation, therefore, the capacitance can NOT be derived by the definition as C=Q/V. Rather, we define dynamic capacitor around bias point! It is a small- signal approximation often referred as junction capacitance or depletion capacitance. QR VVR J j dV dq C = = We can prove that The more general expression for Cj is 2/13/1~ 1 0 0 − ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + = m V V C C m R j j ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ ⎟⎟ ⎠ ⎞ ⎜⎜ ⎝ ⎛ + ⎟ ⎠ ⎞ ⎜ ⎝ ⎛= + == 0 0 0 0 1 2 1 VNN NNq AC V V C W A C DA DAs j R j dep s j εε Course Notes for EE 0257 Analysis and Design of Electronic Circuits Chapter 3: Diodes 5 The pn-junction under forward-bias conditions: If the pn-junction is forwarded biased shown below, then • The external voltage will lower then barrier voltage, which encourage the diffusion of majority carriers from both sides. • Now, when more holes inject into n-region, it increases minority carrier density in n-region: i.e. it increase hole concentration in n-region. • For the same token, when more electron injects into p-region, it increases minority carrier (electron) density in p-region! • The drift current Is stay the same since external voltage won’t change the strength of E-field! • Therefore, we have large forward current! • The excess minority carriers have highest concentration around edge of pn-junction shown above. The follows an exponential decay, using hole (p) in n-region as an example: ( ) ( )[ ] ( ) ( ) T pn V V nnn Lxx nnnnn epxp epxppxp 0 / 00 = −+= −− • Lp is the diffusion length for Si, since minority carriers will recombine with holes. Lp is related to excess-minority- carrier lifetime as: ppp DL τ= Diffusion length for crystalline Si ~1-100 μm. This NON-uniform hole distribution will lead to a diffusion current: ( ) pnT LxxV V n p p p eepL D qJ /0 1 −− ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −= At the edge of pn-junction, x=xn, ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −= 10 T V V n p p p epL D qJ Since the excess minority hole diffuse in n-region, it will recombine with electron to reduce the majority carriers (electron)’s concentration. However, the external current will replenish the majority carriers. In equilibrium, the total current should be the same at any given cross-section (charge conservation!) Therefore, at n-region, total current is: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −= 10 T V V n p p p epL D qJ Using the same analysis, total current in p-region is: ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −= 10 T V V p n n enLn D qJ The total current: ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +=+= 100 TV V n pn p np np eL nD L pD qAAJJI Using AipDin NnnNnp // 2 0 2 0 == : ( ) ⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −≡⎟ ⎠ ⎞ ⎜ ⎝ ⎛ −⎟ ⎟ ⎠ ⎞ ⎜ ⎜ ⎝ ⎛ +=+= 112 TT V V S V V An n Dp p inp eIeNL D NL D qAnAJJI Since kT E i G eBTn − = 32 , therefore IS depends on temperature!