Frequency epone of Aplifier General onideration Miller Effect Aociation of Pole with Node oon ource tage ource Follower ifferential Pair Haan Abouhady Univerity of Pari I eference B. azavi, eign of Analog MO Integrated ircuit, McGraw-Hill, 00. H. Abouhady Univerity of Pari I
Miller Effect Miller Theore Proof with A v Y Y we have A v A v Y Y Y H. Abouhady Univerity of Pari I Y Exaple alculate the put capacitance : F F A F ( A) Av Y hould be calculated at the frequency of teret. To iplify calculation we uually ue low frequency value of Av. Miller theore cannot be ued iultaneouly to calculate put-put tranfer function and the put ipedance. H. Abouhady Univerity of Pari I
Aociation of Pole with Node M N A ( ) N P H. Abouhady Univerity of Pari I N ( ) P( ) P A Aociation of Pole with Node A A N P N 3 P 3 pole: each detered by the total capacitance een fro each node to ground ultiplied by the total reitance een at the node to ground H. Abouhady Univerity of Pari I 3
Exaple alculate the pole aociated with node : The total equivalent capacitance een fro to ground: ( A ) F The pole frequency: ( A) F H. Abouhady Univerity of Pari I Exaple 3 Neglectg channel length odulation, copute the tranfer function of the coon gate tage with paraitic capacitance Paraitic capacitance at node : Input reitance of a coon gate aplifier: g g b G B Pole frequency at node : ( ) G B // g gb Paraitic capacitance at node Y: G B Pole frequency at node : Y ( G B ) H. Abouhady Univerity of Pari I 4
Exaple 3 (cont.) Low-frequency ga of a coon gate tage neglectg channel length odulation: A v0 ( g gb ) ( g g b ) The overall tranfer function i given by: Av 0 Note that if we do not neglect r 0, the put and put node teract, akg it difficult to calculate the pole. H. Abouhady Univerity of Pari I oon ource tage Neglectg channel length odulation and applyg the Miller theore on, we have: The total capacitance at node : G ( A v ) where, A g v The t pole frequency: p ( ( g ) ) G The total capacitance at the put node: B ( Av ) B The nd pole frequency: p ( ) H. Abouhady Univerity of Pari I B 5
oon ource tage The tranfer function: g p p r 0 and any load capacitance can be eaily cluded. ource of error (approxiation): we have not conidered the exitence of zero the circuit the aplifier ga varie with frequency H. Abouhady Univerity of Pari I oon ource : exact Tranfer Function To obta the exact tranfer function: Applyg Kirchoff urrent Law (KL): G ( ) 0 ( ) g 0 B H. Abouhady Univerity of Pari I 6
oon ource : exact t pole After oe anipulation, we get: ξ ( g ) [ ( g ) ( )] G B with ξ G G B B Writg the denoator a: << Aug p p p p H. Abouhady Univerity of Pari I p p p ( g ) ( ) opare thi reult with calculated ug Miller Theore G p p B oon ource : exact nd pole ξ ( g ) [ ( g ) ( )] G B with havg and ξ p G p p p p ( g ) ( ) G B B G B then p ξ p p ( g ) G ( B ) ( ) G G H. Abouhady Univerity of Pari I B B 7
oparion between exact and Miller theore t pole: If ( ) B i negligible exact Miller p p ( ( g ) ) ( ) G ( ( g ) ) G B nd pole: exact p ( g ) G ( B ) ( ) G G B if G >> G p ( g ) ( ) ( ) G G B B B B ( ) p Miller H. Abouhady B Univerity of Pari I oon ource : tranfer function zero After oe anipulation, we get: ξ ( g ) [ ( g ) ( )] G B g z H. Abouhady Univerity of Pari I 8
ource Follower High frequency equivalent circuit Applyg Kirchoff urrent Law (KL) at the put node: G g L at node : ( ) 0 G g ( GL G L ) ( g L G ) g G H. Abouhady Univerity of Pari I ource Follower Input Ipedance I G I gi G L Input Ipedance: G L g G L Note the negative reitance: g G L H. Abouhady Univerity of Pari I 9
ource Follower Output Ipedance Neglectg Applyg KL G g I 0 ( ) 0 G /g Output Ipedance: G G g creae with frequency It conta an ductive coponent H. Abouhady Univerity of Pari I ource Follower Output Ipedance Equivalent t Equivalent circuit of ource follower put ipedance: at at 0 L L L L G G g g G g g g H. Abouhady Univerity of Pari I L 0
ifferential Pair ifferential put: ae a coon ource tage H. Abouhady Univerity of Pari I ifferential Pair oon-mode put: Low frequency A M with M-M iatch: A M g ( g g ) r O3 High frequency A M with M-M iatch: where A M P g // L 3 P ( g g ) r // O G3 B3 B B H. Abouhady Univerity of Pari I