EECS 105 Fall 2003 Lecture 20 Lecture 20 Frequency Response Miller Effect Prof Niknejad Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Lecture Outline Department of EECS Frequency response of the CE as voltage amp The Miller approximation Frequency Response of Voltage Buffer University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Last Time CE Amp with Current Input Can be MOS Calculate the short circuit current gain of device BJT or MOS Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad CS Short Circuit Current Gain MOS Case MOS BJT 0 dB T Ai j g m 1 j Cgd g m j C gs Cgd z gm j C gs Cgd Note Zero occurs when all of gm current flows into Cgd g m vgs vgs j Cgd Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Common Emitter Voltage Amplifier Small signal model omit Ccs to avoid complicated analysis Can solve problem directly by phasor analysis or using 2 port models of transistor OK if circuit is small 1 2 nodes Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad CE Voltage Amp Small Signal Model Two Nodes Easy Same circuit works for CS with Department of EECS r University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Frequency Response KCL at input and output nodes analysis is made complicated due to Z branch see H S pp 639 640 Vout Vin r g m r RS ro roc RL 1 j z 1 j 1 j p1 p2 Low frequency gain Vout Vin r r RS gm Two Poles ro roc RL 1 j 0 1 j 0 1 j 0 gm Zero z T C C Department of EECS Zero gm r r RS ro roc RL Note Zero occurs due to feed forward current cancellation as before University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Exact Poles 1 p1 C Rout C RS r C 1 g m Rout Usually 1 p2 RS r Rout C Rout C RS r C 1 g m Rout These poles are calculated after doing some algebraic manipulations on the circuit It s hard to get any intuition from the above expressions Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Miller Approximation Results of complete analysis not exact and little insight Look at how Z affects the transfer function find Zin Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Input Impedance Zin j I t Vt Vout Z At output node g mVt Rout Vout g mVt I t Rout Why I t Vt AvC Vt Z Z in Vt I t Department of EECS Z 1 AvC University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Miller Capacitance CM Effective input capacitance 1 1 Z in j C M 1 AvC 1 j C 1 j 1 A C vC Cx AV Cx Vin Department of EECS AV Cx Vout 1 Av Cx Cx Vout 1 1 Av Cx Cx University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Some Examples Common emitter source amplifier AvC Negative large number 100 CM 1 AV C C 100C Miller Multiplied Cap has Detrimental Impact on bandwidth Common collector drain amplifier AvC Slightly less than 1 CM 1 AV C C 0 Bootstrapped cap has negligible impact on bandwidth Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad CE Amplifier using Miller Approx Use Miller to transform C RS r Analysis is straightforward now single pole Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Comparison with Exact Analysis Miller result calculate RC time constant of input pole 1 p1 C RS r C 1 g m Rout Exact result C Rout C p1 RS r C 1 g m Rout 1 Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Method of Open Circuit Time Constants This is a technique to find the dominant pole of a circuit only valid if there really is a dominant pole For each capacitor in the circuit you calculate an equivalent resistor seen by capacitor and form the time constant i RiCi The dominant pole then is the sum of these time constants in the circuit p dom Department of EECS 1 1 2 University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Equivalent Resistance Seen by Capacitor For each small capacitor in the circuit Open circuit all other small capacitors Short circuit all big capacitors Turn off all independent sources Replace cap under question with current or voltage source Find equivalent input impedance seen by cap Form RC time constant This procedure is best illustrated with an example Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Example Calculation Consider the input capacitance C1 C CM Open all other small caps get rid of output cap Turn off all independent sources Insert a current source in place of cap and find impedance seen by source RM r RS C 1 RS r C 1 g m Rout Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Common Collector Amplifier Procedure 1 Small signal twoport model 2 Add device and other capacitors Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Two Port CC Model with Capacitors Gain 1 Find Miller capacitor for C note that the base emitter capacitor is between the input and output Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Voltage Gain AvC Across C AvC Rout Rout RL 1 g m RL 1 Rout 1 gm Note this voltage gain is neither the two port gain nor the loaded voltage gain Cin C C M C 1 AvC C 1 Cin C C 1 g m RL Cin C Department of EECS University of California Berkeley EECS 105 Fall 2003 Lecture 20 Prof A Niknejad Bandwidth of CC Amplifier Input low pass filter s 3 dB frequency p 1 C RS Rin C 1 g m RL Substitute favorable values of RS RL RS 1 g m p 1 RL 1 g m C 1 g m C C g m 1 BIG Model not valid at these high frequencies p g m C T Department of EECS University of California Berkeley
View Full Document
Unlocking...