Lecture 13Cascoding Cascode?Cascode AmplifierReview: Sinusoidal AnalysisHigh Frequency “Roll-Off” in AvAv Roll-Off due to CLFrequency Response of the CE StageAmplifier Figure of Merit (FOM)Bode PlotBode Plot ExamplePole Identification ExampleHigh-Frequency BJT ModelBJT High-Frequency Model (cont’d)Example: BJT CapacitancesTransit Frequency, fTDealing with a Floating CapacitanceMiller’s TheoremMiller MultiplicationApplication of Miller’s TheoremSmall-Signal Model for CE Stage… Applying Miller’s TheoremDirect Analysis of CE StageInput Impedance of CE StageEE105 Fall 2007 Lecture 13, Slide 1 Prof. Liu, UC BerkeleyLecture 13OUTLINE•Cascode Stage: final comments•Frequency Response–General considerations–High-frequency BJT model–Miller’s Theorem–Frequency response of CE stageReading: Chapter 11.1-11.3ANNOUNCEMENTS•Midterm #1 (Thursday 10/11, 3:30PM-5:00PM) location:•106 Stanley Hall: Students with last names starting with A-L•306 Soda Hall: Students with last names starting with M-Z•EECS Dept. policy re: academic dishonesty will be strictly followed!•HW#7 is posted online.EE105 Fall 2007 Lecture 13, Slide 2 Prof. Liu, UC BerkeleyCascoding Cascode?•Recall that the output impedance seen looking into the collector of a BJT can be boosted by as much as a factor of , by using a BJT for emitter degeneration.•If an extra BJT is used in the cascode configuration, the maximum output impedance remains ro1. 11211121121||||)]||(1[ooomoutooomoutrrrrgRrrrrrgR1111max,121121||)]||(1[oomoutooomoutrrrgRrrrrrgREE105 Fall 2007 Lecture 13, Slide 3 Prof. Liu, UC BerkeleyCascode Amplifier•Recall that voltage gain of a cascode amplifier is high, because Rout is high.•If the input is applied to the base of Q2 rather than the base of Q1, however, the voltage gain is not as high.–The resulting circuit is a CE amplifier with emitter degeneration, which has lower Gm. 21211rrgrgAomomv 21221oomminomrrggviGEE105 Fall 2007 Lecture 13, Slide 4 Prof. Liu, UC BerkeleyReview: Sinusoidal Analysis•Any voltage or current in a linear circuit with a sinusoidal source is a sinusoid of the same frequency ().–We only need to keep track of the amplitude and phase, when determining the response of a linear circuit to a sinusoidal source.•Any time-varying signal can be expressed as a sum of sinusoids of various frequencies (and phases). Applying the principle of superposition:–The current or voltage response in a linear circuit due to a time-varying input signal can be calculated as the sum of the sinusoidal responses for each sinusoidal component of the input signal.EE105 Fall 2007 Lecture 13, Slide 5 Prof. Liu, UC BerkeleyHigh Frequency “Roll-Off” in Av •Typically, an amplifier is designed to work over a limited range of frequencies.–At “high” frequencies, the gain of an amplifier decreases.EE105 Fall 2007 Lecture 13, Slide 6 Prof. Liu, UC BerkeleyAv Roll-Off due to CL •A capacitive load (CL) causes the gain to decrease at high frequencies.–The impedance of CL decreases at high frequencies, so that it shunts some of the output current to ground.LCmvCjRgA1||EE105 Fall 2007 Lecture 13, Slide 7 Prof. Liu, UC BerkeleyFrequency Response of the CE Stage•At low frequency, the capacitor is effectively an open circuit, and Av vs. is flat. At high frequencies, the impedance of the capacitor decreases and hence the gain decreases. The “breakpoint” frequency is 1/(RCCL).1222LCCmvCRRgAEE105 Fall 2007 Lecture 13, Slide 8 Prof. Liu, UC BerkeleyAmplifier Figure of Merit (FOM)•The gain-bandwidth product is commonly used to benchmark amplifiers. –We wish to maximize both the gain and the bandwidth.•Power consumption is also an important attribute.–We wish to minimize the power consumption. LCCTCCCLCCmCVVVICRRg1 1nConsumptioPower BandwidthGainOperation at low T, low VCC, and with small CL superior FOMEE105 Fall 2007 Lecture 13, Slide 9 Prof. Liu, UC BerkeleyBode Plot•The transfer function of a circuit can be written in the general form•Rules for generating a Bode magnitude vs. frequency plot:–As passes each zero frequency, the slope of |H(j)| increases by 20dB/dec.–As passes each pole frequency, the slope of |H(j)| decreases by 20dB/dec.212101111)(ppzzjjjjAjHA0 is the low-frequency gainzj are “zero” frequenciespj are “pole” frequenciesEE105 Fall 2007 Lecture 13, Slide 10 Prof. Liu, UC BerkeleyBode Plot Example•This circuit has only one pole at ωp1=1/(RCCL); the slope of |Av|decreases from 0 to -20dB/dec at ωp1. •In general, if node j in the signal path has a small-signal resistance of Rj to ground and a capacitance Cj to ground, then it contributes a pole at frequency (RjCj)-1LCpCR11EE105 Fall 2007 Lecture 13, Slide 11 Prof. Liu, UC BerkeleyPole Identification ExampleinSpCR11LCpCR12EE105 Fall 2007 Lecture 13, Slide 12 Prof. Liu, UC BerkeleyHigh-Frequency BJT Model•The BJT inherently has junction capacitances which affect its performance at high frequencies.Collector junction: depletion capacitance, C Emitter junction: depletion capacitance, Cje, and also diffusion capacitance, Cb.jebCCC EE105 Fall 2007 Lecture 13, Slide 13 Prof. Liu, UC BerkeleyBJT High-Frequency Model (cont’d)•In an integrated circuit, the BJTs are fabricated in the surface region of a Si wafer substrate; another junction exists between the collector and substrate, resulting in substrate junction capacitance, CCS.BJT cross-section BJT small-signal modelEE105 Fall 2007 Lecture 13, Slide 14 Prof. Liu, UC BerkeleyExample: BJT Capacitances•The various junction capacitances within each BJT are explicitly shown in the circuit diagram on the right.EE105 Fall 2007 Lecture 13, Slide 15 Prof. Liu, UC BerkeleyTransit Frequency, fT•The “transit” or “cut-off” frequency, fT, is a measure of the intrinsic speed of a transistor, and is defined as the frequency where the current gain falls to 1.CgfmT2Conceptual set-up to measure fTinininZVI inmoutVgI inmTinTminminoutCgCjgZgII11EE105 Fall 2007 Lecture 13, Slide 16 Prof.
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