Lecture 13 ANNOUNCEMENTS 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 OUTLINE Cascode Stage final comments Frequency Response General considerations High frequency BJT model Miller s Theorem Frequency response of CE stage Reading Chapter 11 1 11 3 EE105 Fall 2007 Lecture 13 Slide 1 Prof Liu UC Berkeley Cascoding 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 Rout 1 g m1 ro 2 r 1 ro1 ro 2 r 1 Rout g m1ro1 ro 2 r 1 ro1 If an extra BJT is used in the cascode configuration the maximum output impedance remains ro1 Rout 1 g m1 ro 2 r 1 ro1 ro 2 r 1 Rout max g m1ro1r 1 ro1 EE105 Fall 2007 Lecture 13 Slide 2 Prof Liu UC Berkeley Cascode Amplifier Recall that voltage gain of a cascode amplifier is high because Rout is high Av g m1ro1 g m 2 ro1 r 2 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 io gm2 Gm vin 1 g m 2 ro1 ro 2 EE105 Fall 2007 Lecture 13 Slide 3 Prof Liu UC Berkeley Review 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 timevarying 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 4 Prof Liu UC Berkeley High 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 5 Prof Liu UC Berkeley Av 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 1 Av g m RC j C L EE105 Fall 2007 Lecture 13 Slide 6 Prof Liu UC Berkeley Frequency 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 Av EE105 Fall 2007 Lecture 13 Slide 7 g m RC 2 C 2 L 2 R C 1 Prof Liu UC Berkeley Amplifier 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 1 g m RC RC C L Gain Bandwidth Power Consumption I CVCC 1 VT VCC C L Operation at low T low VCC and with small CL superior FOM EE105 Fall 2007 Lecture 13 Slide 8 Prof Liu UC Berkeley Bode Plot The transfer function of a circuit can be written in the general form j j 1 1 z1 z 2 H j A0 j j 1 1 p1 p2 A0 is the low frequency gain zj are zero frequencies pj are pole frequencies 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 EE105 Fall 2007 Lecture 13 Slide 9 Prof Liu UC Berkeley Bode Plot Example This circuit has only one pole at p1 1 RCCL the slope of Av decreases from 0 to 20dB dec at p1 1 p1 RC C L 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 1 EE105 Fall 2007 Lecture 13 Slide 10 Prof Liu UC Berkeley Pole Identification Example 1 p1 RS Cin EE105 Fall 2007 p2 Lecture 13 Slide 11 1 RC C L Prof Liu UC Berkeley High 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 C Cb C je EE105 Fall 2007 Lecture 13 Slide 12 Prof Liu UC Berkeley BJT 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 EE105 Fall 2007 BJT small signal model Lecture 13 Slide 13 Prof Liu UC Berkeley Example 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 14 Prof Liu UC Berkeley Transit 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 Conceptual set up to measure fT I out g mVin Vin I in Z in 1 I out 1 g m Z in g m I in j T Cin T gm Cin gm 2 fT C EE105 Fall 2007 Lecture 13 Slide 15 Prof Liu UC Berkeley Dealing with a Floating Capacitance Recall that a pole is computed by finding the resistance and capacitance between a node and GROUND It is not straightforward to compute the pole due to C 1 in the circuit below because neither of its terminals is grounded EE105 Fall 2007 Lecture 13 Slide 16 Prof Liu UC Berkeley Miller s Theorem If Av is the voltage gain from node 1 to 2 then a floating impedance ZF can be converted to two grounded impedances Z1 and Z2 V1 V2 V1 V1 1 Z1 Z F Z F ZF Z1 V1 V2 1 Av V1 V2 V2 V2 1 Z 2 Z F Z F ZF Z2 V1 V2 1 1 EE105 Fall 2007 Lecture 13 Slide 17 Av Prof Liu UC Berkeley Miller Multiplication Applying Miller s theorem we can convert a floating capacitance between the input and output nodes of an amplifier into two grounded capacitances The capacitance at the input node is larger than the original floating capacitance A0 Av ZF Z2 1 1 …
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