Microelectronic Circuits Study Guide (Chapter 6)

Chapter 6: Binary Junction Transistors (BJTs) BJTs, like MOSFETs, are useful as controlled sources, as switches, and as logic inverters - BJTs were first discovered after MOSFETs, but were more useful for a while until MOSFET manufacturing techniques were improved - however, BJTs are still more useful in some cases, such as extreme environmental conditions and very-high-frequency devices (e.g., emitter-coupled logic); other contexts use MOSFETs in conjunction with BJTs 6.1: Device Structure and Physical Operation Two types of BJTs are possible: pnp BJTs and npn BJTs - the npn BJT is manufactured by creating a highly doped n-type emitter, a lightly doped p type base, and a lightly doped n-type collector, with metal contacts forming terminals connected to each region (pnp BJTs simply reverse the doping types of the regions) - most of the following discussion will focus on the npn BJT, but the same properties apply to the pnp BJT The BJT has two pn junctions: the emitter-base junction (EBJ) and the collectorbase junction (CBJ) - the relative voltages of the terminals determine whether each junction is forward- or reverse-biased, and thus the operating properties of the device: EBJ Reverse Forward Reverse Forward CBJ Reverse Reverse Forward Forward Mode Cutoff Forward Active Mode Reverse Active Mode Saturation Typically, the forward active mode is used when the transistor is configured as an amplifier, and the saturation and cutoff modes are used when the transistor is configured as a switch 47 Forward-active mode: This mode arises in the npn BJT when vE < vB < vC , exhibiting a conventional current from collector to emitter In the forward active mode, the EBJ is forward-biased and the CBJ is reversebiased - this forward bias creates two types of current: electrons injected from the emitter into the base, and holes injected from the base into the emitter (the doping levels create a much higher electron current than hole current) the injected electrons diffuse through the base region, with the concentration steadily diminishing across the length of the base (reduced a bit further by recombination) - the electron concentration just beyond the EBJ is defined as: vBE np (0) = np0 e VT , where: np0 is the thermal equilibrium value of majority carriers in the base region This injection also gives rise to an electron diffusion current: p (x) = AE qDn (− npW(0) ), where In = AE qDn dndx AE = the cross-sectional area of the emitter-base junction Because electrons flow left-to-right (emitter-to-base), this diffusion gives rise to a conventional current from right-to-left Forward-active mode collector current: Because the CBJ is reverse-biased, injected electrons that diffuse across the base to reach the CBJ are swept across the junction due to the barrier voltage - this gives rise to a collector current, which is defined as: VBE iC = IS e VT , where IS = saturation current, which is defined as: 2 N ni IS = AE qDN nWp0 = AENqD Aw Notably, the collector current iC is independent of VCB ; as long as this value is positive (to maintain reverse-bias), the saturation and collector currents are not dependent on the actual voltage - the linear dependence on the area enables otherwise-identical devices to exhibit currents as a ratio (e.g., if the same voltage is applied to two BJTs with a 1:2 area ratio, the current through each BJT will also have a 1:2 ratio) 48 Forward-active mode base current: The base current iB has two components: iB1 , the injection of holes from the base region into the emitter region, and iB2 , the supply of holes from the terminal in response to the loss of holes from recombination - the total base current is defined as: iB = iB1 + iB2 VBE Since iB is proportional to e VT , just like iC , the base current is always proportional to the emitter current: iB =iC , where β β = the common-emitter current gain, which is a transistor parameter that is usually in the range of 50 to 200 - it is desirable to keep β high - this factor is inversely proportional to the length of the base region (hence W is usually kept small), and directly proportional to the doping ratio of the base and emitter NA ) regions ( N D Forward-active mode current relationships: The current through the npn BJT in forward-active mode creates a conventional current from collector to emitter - the total emitter current is defined as: VBE iE = iC + iB = β+1 i = β+1 I S e VT β C β To simplify this equation, we can define a parameter α as the common-base current gain: β α , such that α = β+1 (or conversely, β = 1− iE = iS e α vBE VT Forward-active mode equivalent-circuit models: When a positive VBE voltage is applied to an npn BJT, the collector emits a constant current that is independent of VCB as long as the CBJ remains reverse-biased ( VC B ≥ 0 ) because the base current is ideally very small, iC ≈ iE - the npn BJT therefore operates as a constant-current source, where the current is defined by VBE based on this behavior, four equivalent circuit models are possible: 49 This model is a voltage-controlled current source - note that the current in this model does not scale linearly, but exponentially, with the measured voltage This model is a current-controlled current source - again, the current in this model does not scale linearly, but exponentially, with the measured current the gain between iE (as input) and iC (as output) is determined by α, which is why α is called the common-base current gain 50 This model is a two-port voltage-controlled current source This model is a two-port current-controlled current source - the gain between iB (as input) and iC (as output) is determined by β, which is why β is called the common-emitter current gain A typical npn BJT is formed as follows: 51 Unlike a MOSFET which is structurally symmetric and reversible, the structural asymmetry makes this device non-reversible, with α ≈ 1 and a large β value Reverse-active mode: This mode arises in the npn BJT when vE > vB > vC - the BJT in reverse-active mode operates similarly to forward-active mode, but with a much lower value of β, making this mode undesirable Cutoff mode: This mode arises in the npn BJT when vE > vB < vC , such that both junctions are reversed-biased - in this mode, the reverse biases of the EBJ and CBJ effectively prevent the flow of current Saturation mode: This mode arises in the npn BJT when vE < vB > vC , such that both junctions are forward-biased - note that the forward-active mode of the npn BJT can be maintained as long as vCB ≥ −0.4 V (since forwardbias of the pn junction only occurs at +4 V) - below this value, the npn BJT is in saturation mode - the collector current is reduced, and the base current increases, dependent upon vC B : vBE vBC iC = IS e VT − ISC e VT vBE vBC iB = IβS e VT + ISC e VT This relationship causes the value of β to change based on vBC ; i.e., vBC “forces” β to a value lower than the constant value of β in forward-active mode - the resulting new value of β is called βforced , and is defined as: βforced = iiBC |saturation ≤ β This provides two ways to determine whether the BJT is in saturation mode: either vCB < −0.4 V, or iiC < β B The depth of the saturation mode can be expressed as: vCEsat = vBE − vC E , where vCEsat = 0.3 V indicates that the transistor is at the edge of saturation, and vCEsat ≤ 0.2 V indicates that the transistor is deep in the saturation region The saturation-mode BJT can be modeled as follows: The pnp BJT: 52 The pnp BJT works in a similar manner as the npn BJT, except that the current is mainly conducted by holes, and conventional current is from the emitter to the collector - also, a base current runs out of the BJT rather than into the base region 6.2: Current-Voltage Characteristics npn and pnp BJTs exhibit current flow in opposite directions, and are represented by the direction of the arrow (always pointing from positive to negative) - currents are always measured in the positive direction - the following diagrams show the currents of npn and pnp BJTs respectively: 53 Collector-base reverse current: The reverse current across the collector-base junction, with the emitter open-circuited, is denoted ICBO ; the value is typically in the nA range, and is dependent upon VC B , doubling for each 10◦ C increase BJT iC − vBE Characteristic: Since iC varies logarithmically with vBE and is temperature-dependent, the BJT exhibits the following relationship: Early effect: The voltage vCE has a small but positive relationship with iC , which also scales with higher values of vBE - iC − vBE is a straight line, and, extrapolating backward, we find a common point −VA that defines the relationship: This relationship occurs because of the base-width modulation effect: raising vCE increases the reverse-bias voltage, increases the width of the depletion region, and decreases the effective base width (i.e., the width of the transistor 54 1 acting as the base region); since IS W , a shorter effective base width increases the current - the Early effect can be modeled as follows: VBE iC = IS e VT (1 + vVCE ) A This can also be modeled as output resistance: CE ro = VA +V IC ′ We can also define IC as the collector current with the Early effect neglected, and that ro = IV′A C C ; i.e., vary iB by a little, and notice the We can also measure β as β = δi δiB change in iC - this property actually exhibits differences in alternating-current and direct-current circumstances, but we can disregard this difference for now In saturation, ICsat = βforced IB , where βforced < β - as a result, the Early effect is attenuated in saturation, but leads to significant differences in the active mode due to larger values of β BJT Circuits at DC Examples of BJT circuits operating in direct-current scenarios: Presume that VBE = 0.7V; VCEsat = 0.2V when saturated; and disregard Early effect - the first question is: Which mode is the transistor in? • First presume that the BJT is in forward-active mode, and verify that behavior matches VCB > −0.4V • If not, presume that the BJT is in saturation mode, and verify that βforced < β 55 IC IB = 6.4: Applying the BJT in Amplifier Design Natively, the BJT operates as a transconductance amplifier (i.e., a voltagecontrolled current source): vBE controls IC - these types of amplifiers can easily be converted to a voltage amplifier (i.e., a voltage-controlled current source) by inserting a resistor RC at the collector and measuring its voltage drop the relationship between input voltage vBE and output voltage iC RC does not change linearly (the response depends on whether vBE places the BJT in the cutoff mode, active mode, or saturation mode), but can be converted to a linear amplifier over a small range Simple amplifier and its voltage transfer characteristic (vBE → vCE : This transistor has output vCE = VCC − iC RC - the active mode shows strong gain (steep slope) with output: vBE vCE = VC C − RC IS e VT While this range, described broadly, is nonlinear, it becomes more linear on a small scale - we can make use of this region as a linear amplifier by confining our input to this range Biasing the BJT: A point Q along this curve can be selected in the middle of the range, and a constant voltage source VBE can be applied to bias the base up to this point: 56 At this point, the BJT exhibits output: VBE I C = IS e VT Then we apply to the base a second voltage source, vbe , which carries a smallsignal variation - the total instantaneous value applied to the base is: vBE (t) = VBE + vbe (t) This variance produces linear output vCE as long as vbe is kept small; linearity decreases with higher magnitude of vbe The voltage gain AV of the amplifier is: dvCE AV = dv |vBE ≈VBE BE The voltage gain can also be expressed as: IC AV = − V T R C This indicates that the voltage gain is proportional to the voltage drop of RC , so we can increase the gain by increasing RC - however, if VCC is constant, increasing RC correspondingly decreases VCE and pushes the quiescent point toward the cutoff region, thus reducing the maximum swing (specifically, head room) of the small signal Determining the VTC by graphical analysis: 57 We can determine the VTC by graphing vCE vs.iC , for various values of vBE , and superimposing a line representing VRC - this line (the “load line”) begins at the horizontal axis at vCE = VCC , and has a negative slow − R1C - the intersection of the load line with each value represents the voltage of VCE for each value of vBE 6.5: Small-Signal Operation and Models When evaluating circuit models for small-signal amplification, first set the small signal vbe to zero, and evaluate the circuit to determine its direct-current bias VBE - applying a small-signal voltage over the direct-current bias results in the following models: vBE = VBE + vbe Collector current: The collector current in the small-signal model is defined as: VBE vbe iC = IS e VT e VT If vbe << VT , then the following approximations can be used: ) iC ≈ IC (1 + Vvbe T iC = IC + VIC vbe T This latter term is the signal component of the combined signal: ic = VIC vbe T This can be rewritten using transconductance: gm = VICT ic = gm vbe Transconductance defines a linear, positive relationship between vbe and iC : Base current: As usual, the base current is a factor of the collector current, but 58 we can now separate the base current into the direct-current component and the small-signal component: iB = iβC = IβC + ICβVvbe = IβC (1 + vVbe = IβC + vbeβgm T T The small-signal component of the base current is: ib = gβm vbe The small-signal input resistance is defined as the resistance between the base and the emitter, looking into the base: = g β = VI T rπ = vibe b B m Emitter current: The total emitter current can also be broken into components: iE = iαC = IαC + iαc The small-signal emitter resistance is defined as the resistance between the base and the emitter, looking into the emitter: re = vibe = VIET = gαm ≈ g1m e The base resistance rπ and emitter resistance re are related as follows: vbe = ib rπ = ie re rπ = iieb re Voltage Gain: In the small-circuit model, the amplifier is operating as a transconductance amplifier, where vbe causes a proportional current ic = gm vbe to flow - the amplifier can be converted to a voltage amplifier by positioning a resistor at the conductor: vCE = VCC − iC RC = VCE − ic RC The voltage gain of the amplifier is measured as: AV = vvce = −gm RC = − ICVRTC be Hybrid π models: The small-signal BJT amplifier can be equivalently represented by a hybrid π model of the circuit, with separate branches for ic and ib , and the collector current represented as either ic = gm vbe or ic = βib - this model explicitly includes the base resistance, rπ 59 T model: The small-signal BJT amplifier can also be equivalently represented by a T model, with the collector and base feeding into the emitter - this model explicitly includes the emitter resistance, re 60 Application of small-signal equivalent circuits: The process for evaluating a circuit using a small-signal model is as follows: • Determine the DC operating point and the DC collector current IC • Calculate the parameters of the small-signal model: gm = β ; re = VITE = gα g m IC VT ; rπ = m • Substitute a small-signal equivalent circuit • Analyze the circuit to determine the required quantities Early effect in small-signal models: The models above disregard the Early effect, but this can be modeled by supplementing each model with a resistor ro , with the following value: r0 = IVCA The Early effect reduces both vo and AV : vo = −gm vbe(RC ||ro ) 6.6: Basic BJT Amplifier Configurations Three basic BJT amplifier configurations are possible - the small-signal version of each amplifier can be substituted with this model: 61 Each amplifier has several properties: • Input resistance: Rin = vi ii • Output resistance, when vsig = 0: : Ro = • Voltage gain of the amplifier: Av = vx ix vo vi • Voltage gain of the amplifier under open-circuit conditions: Avo = • Overall voltage gain: Gv = vo vsig Common-emitter (CE) amplifier: The equivalent circuit for the common-amplifier BJT is: • Input resistance: Rin = rπ • Output voltage: vo = −gm vπ )(RC ||ro ) 62 vo | vi RL =∞ • Open-circuit voltage gain: Avo = −gm (RC ||ro ) • Output resistance: Ro = RC ||ro rπ • Voltage gain: Av = −gm (RC ||RL ||ro ) Overall voltage gain: Gv = − rπ +R gm (RC ||RL ||ro ) sig For the common-emitter amplifier, input resistance tends to be low (increasing the input resistance decreases the gain), and output resistance and open-circuit voltage gain are high The properties of the amplifier change if a resistor is positioned at the emitter - this changes the circuit in the following ways: • The input resistance is then reflected as: Rin = (β + 1)(re + Re ) e The input resistance thus increases by a factor of R - this property is re termed the “resistance-reflection rule”: i.e., the input resistance reflects the resistance of the emitter • The voltage gain is reduced by a factor of gm Re - the gain can be maintained by increasing the input signal proportionally by a factor of gm Re The effect of the emitter resistor is to reduce the dependence of Gv on β, and to improve the high-frequency response of the amplifier Common-base (CB) amplifier: For common-base amplifiers, the Early effect is typically small and is disregarded to simplify the analysis • Input resistance: Rin = re 63 • Output voltage: v0 = −αie Rc • Open-circuit voltage gain: Avo = gm RC • Output resistance: Ro = RC • Voltage gain: Av = gm (RC ||RL ) - note that the low input resistance reduces the magnitude of the input signal, and the achievable gain C ||RL • Overall voltage gain: Gv = α RRsigh +re The gain of this amplifier is very small, but it maintains a good frequency response at higher frequencies, so it is often used in combination with other amplifier types Common-collector (CE) amplifier: The common-collector amplifier functions as an emitter follower, and is useful when a voltage signal is presented with a high input resistance, such that attaching a load directly to the input causes a very small signal across the load - the CE amplifier uses the input signal at the base to drive a current through the emitter with a much lower output resistance • Input resistance: Rin = β + 1)(re + RL ) (another example of resistance reflection) • Open-circuit voltage gain: Avo = 1 • Output resistance: Ro = re 64 L • Voltage gain: Av = RLR+r e • Overall voltage gain: Gv = (β+1)RL (β+1)(RL +re )+Rsig 6.7: Biasing in BJT Amplifier Circuits A BJT amplifier is biased to ensure that the gain of the amplifier remains constant across all frequencies of interest - two biasing solutions that do not work well: applying a fixed VBE (very small deviations in VBE lead to large changes in the output), and providing a constant base current (variations in β in different circuits lead to significant differences in gain) Classical discrete-circuit bias: If only one voltage source is available, a fourresistor network is used as a voltage divider to provide a fixed voltage the the base This circuit can be evaluated by substituting the left half with its Thévenin equivalent, and then applying KVL from the base voltage to the emitter ground - this circuit can be made more resistant to variations in temperature and β by RB - this arrangement provides negative making VBB >> VBE and RE >> β+1 feedback: if RE increases, the rise in VE causes a decrease in VBE , which reduces the flow of current through the transistor; conversely, if RE falls, the lower VE and higher VBE cause more current to flow across the resistor Two-power-supply version: If two power supplies VCC , −VEE are available, the base can be grounded (resistor RB is only needed if the signal is capacitively coupled to the base) 65 Collector-to-base feedback resistor: A resistor connecting the collector and base can provide negative feedback - this circuit can be analyzed by applying KVL over VCC , RC , RB , VBE , andtheemitterground : − VCC + IE RC + IB RB + VBE = 0 Constant-current source: A constant current source can be applied from the emitter Current mirror: Two identical transistors can be connected at the base and emitter, and a positive voltage is applied to RC of one transistor - this creates a reference current IREF through R that must be matched by the current I in the other transistor Since the transistors are identical, the base currents and emitter currents are identical; the reference current IREF is determined by applying KVL from VCC 66 through the collector-base connection, over VBE , and to −VEE : BE +VEE I = IREF = VC C −VR 6.8: Discrete-Circuit BJT Amplifiers The constant-current biasing model can be combined with the amplifier types discussed in 6.6: When combined with any model, capacitors are used to connect the AC components for the amplification (the capacitors connected to the input and output terminals are called “coupling” capacitors; the capacitor coupled to the ground is called a “bypass” capacitor) Biased common-emitter circuit: 67 Biased common-emitter circuit with unbypassed resistance: Biased common-base circuit: 68 Biased common-collector (voltage follower) circuit: Frequency response: Common-emitter amplifiers typically demonstrate constant gain over a significant frequency range (the bandwidth of the amplifier) - at lower frequencies, the gain and frequency response are diminished because the impedances of the coupling and bypass capacitors begin attenuating the lowfrequency signal; at higher frequencies, the capacitance of the pn junction becomes significant 6.9: Transistor Breakdown and Temperature Effects The maximum voltage applicable to a BJT is limited by the breakdown voltage of the reverse-biased junction - the breakdown voltage is typically around 50 V breakdown of the collector-base junction is typically not destructive, but breakdown of the emitter-base junction causes a runaway current that permanently reduces β; however, the EBJ can still be used as a zener diode, which does not depend on β 69 One complexity that has been disregarded is that β is dependent on the bias current, but the bias current is typically chosen to make β as large as possible - β is also temperature-dependent, which affects the transistor when operating at high power levels 70