Miller Opamp
Desin Of The Miller Opamp The Miller opamp is made up of Input differential stae Simple MOS OTA A second ain stae ommon Source Amplifier The desin of a Miller opamp is beneficial as a learnin tool, it requires Knowlede of hih impedance nodes and parasitic caps Knowlede of common source amplifiers Knowlede of source followers Knowlede of differential amplifiers Good biasin techniques Understandin Bode plots Understandin the Miller effect Understandin of offsets as related to matchin and so on...
Bode Diarams Bode diarams are an extension of Nyquist plots Bode diarams describe the manitude and phase response of the ain at various frequencies The manitude and phase of the ain are plotted vs. frequency The Y-axis is in Decibels or 0 lo(v o /V i ) The X-axis is in decades Bode diarams are a powerful tool They can be used for system analysis System compensation Stability check In order to plot Bode diarams effectively must start with simple systems Understand the behavior of zeros at hih and low frequencies Understand the behavior of poles at hih and low frequencies All transfer functions will be based on some combination thereof 3
Behavior Of A System Zero In LHP s + a s jω Puttin it all toether At low frequencies relative to a the term a dominates At LF --> 0lo(a) At hih frequencies the term jω dominates At HF --> 0lo( ω ) But we also have a phase term j at hih frequencies This term was not present at low frequencies Phase (de); Manitude (db) 80 60 40 0 00 50 Bode Diaram; (s+0) 0 0-0 0 0 0 0 3 Frequency (rad/sec) j represents a 90 deree phase shift Finally, at sja, s+a becomes a+ja This repesents 45 derees of phase Note that the phase plot starts a decade earlier and ends a decade later than 0 4
Dealin With A RHP Zero A RHP zero must be dealt with a little differently than a LHP zero s-a For very low frequencies w.r.t. a only the term -a will dominate -a represents a with 80 derees of phase shift a a 80 Therefore at low frequencies there is 80 derees phase associated with the response At hih frequencies s-->jω dominates representin 90 derees of phase So start with 80 derees of phase, end at 90 derees of phase The point of transition beins at.a with a slope of -45 derees per decade o Phase (de); Manitude (db) 80 60 40 0 00 50 00 Puttin it all toether Bode Diarams 50 0-0 0 0 0 0 3 Frequency (rad/sec) A RHP zero is troublesome because it adds phase to a system A problem in amplifier desin when tryin to achieve ood phase marin 5
Behavior Of A LHP Pole LHP pole analysis is similar to LHP zero analysis s + a s jω At low frequencies the term /a dominates At hih frequencies /jω dominates /j represents -90 derees of phase Therefore, no phase at low frequencies -90 derees of phase at hih frequencies -45 derees per decade around break point The manitude plot now decreases at -0dB/decade Do not consider RHP poles because that represents an unstable system Phase (de); Manitude (db) -0-30 -40-50 -60 0-50 Puttin it all toether Bode Diarams -00 0-0 0 0 0 0 3 Frequency (rad/sec) 6
The Three Stae Miller Opamp Vdd M3 I bias M4 M5 Vi- M M Vi+ c M M0 M9 M6 M7 Rc M8 M l Vss Two desin methodoloies will be investiated The first desin will not include the compensation resistor in the miller path The second desin will include the compensation resistor This opamp structure will accept a differential sinal It will provide a sinle ended output There are two hih impedance nodes that provide ain 7
GBW Desin Equation More To ome Low frequency ain of differential, SA, and Source Follower staes M3 Av m A Z out ( r r ) v m 8 o 5 // o 8 Vi- M V M Vi+ V c V -A A3 Vout A v3 m + m ds + ds M6 M7 Node V will experience the Miller effect at low frequency eq c( + A v ) Zout ro // ro 7 // s Z out s A c eq v Assumin A v3 is close to A ( s) A A v v A v A () s A ( jω ) v un v3 A f v s un m c A v π m 8
Analyzin The Nodes, Exclude Rc and c Vdd M3 I M4 M5 bias M0 M9 Vi- M M6 M7 M Rc Vi+ c M8 3 M M l Vss Stae Stae Node is a low impedance node due to the diode connection f p π n f p m6 m6 π n Node is a hih impedance node f p π ( ro // ro 7 ) n Node 3 is a hih impedance node f p3 π ( ro 5 // ro 8 ) n3 9
A Three Pole System Without ompensation Phase (de); Manitude (db) 00 50 0-50 -00 0-00 -00 Bode Diaram For A Three Pole System -300 0-0 0 0 0 0 3 0 4 Frequency (rad/sec) Without compensation this system representin an opamp has no phase marin and can be potentially unstable Barkhausen riteria avoidance meter Phase and Gain marins are an extension of Nyquist diarams They relate system stability information Phase Marin Go to 0dB on the ain plot Draw a line straiht down to the phase plot The amount of derees above 80 is the phase marin Gain Marin Go to 80 derees on the phase plot Draw a line straiht up to the ain plot The amount of db below zero is the ain marin 0
Addin ompensation apacitance Produces A Dominant Pole Purposes of addin compensation capacitance f Drowns out the effect of poorly controlled parasitics Moves the -3bB point to a much lower frequency Seperates the two dominant poles Improves phase marin Improves stability With the addition of a miller capacitance the -3dB point chanes from f p to π ( ro // ro 7 ) n The GBW is iven by multiplyin f p by the open loop ain GBW π A v m 8( r o 8 // r o 5 ) m ( ro // ro 7 ) m8( ro 8 // ro 5 ) ( r o // r o 7 )( + m 8( r o 8 // r o 5 )) c GBW m p π ( r ) π o // ro 7 + Av c c
Understandin The Effect Of The Non-Dominant Pole Vdd M3 I bias M4 M5 Vi- M M Vi+ c 3 Rc M0 M9 M6 M7 M8 L Vss At hih frequencies (close to unity ain) c acts as a short circuit This action makes M8 behave as a diode connected transistor The impedance at node 3 becomes approximately / m8 f p3 π m8 L
Phase Marin And The Desin Process With the c in place the phase marin can be determined usin PM 90 o tan GBW f p 3 For stability, settlin time, and limitin the amount of overshoot, a phase marin of 7 derees and above is a ood, tiht desin requirement 7 o 90 o tan GBW f p 3 o ( ) GBW f p 3 tan 8 f p 3 3GBW With this and the GBW equation the desin process can be started Must however take a closer look at compensation 3
c Produces A RHP Zero Addin Phase La s c v v o R eq r o 7 // r o m v id m8 v R eq s eq R eq s eq R r r eq o 5 // o 8 + + eq db db7 s8 + eq db8 + db5 L Writin the nodal equations for the circuit above locates the RHPZ v ( s s + ) + v v s 0 v ( s s + ) + v v s 0 eq + c eq m8 id o c o eq + c eq m8 c The above two equations in two unknowns can be solved to yield v v o i s R eq R eq ( + + ) + s( ( + ) R + ( + ) R + R R ) + m m8 R eq R eq s m8 m8 4
ompensatin The ompensation If the input stae transconductance is comparable to the output stae s, the circuit will suffer The unity ain frequency and the zero will occur close toether Since the zero is in the RHP the phase marin will be further deraded Must compensate for the RHP zero to achieve ood phase marin ompensation is often provided by insertin a series resistor in front of c Unfortunately this small addition has a bi mathematical impact v Rc v3 s c v o m v id R eq s eq m8 v R eq s eq 5
What Now Addin a series resistor will modify the zero location ω z R m8 Now there are possibilities The zero can be eliminated Or be shifted to the LHP Must be careful in selectin resistor values Too hih a resistance will eliminate the hih frequency short circuit of c Keep compensation resistance values to very low hundreds of ohms at most Use a small width device if usin a triode FET There are alternate strateies such as includin a buffer to block the forward current A buffer has the added advantae of providin a level shift The added level shift can be used to bias a device capacitor 6
Vdd M4 M3 ommon Mode Input Rane M5 Assume Vdd3.0, Vtn0.5 Vtp0.56 and all Von0. Ibias Vi- M M Vi+ c Then VI,max3.0-0.96.04V VI,min0.+0.5-0.560.54V Vss M6 M7 Rc M8 L Which leaves about.85v of common mode input rane M3 will o into triode when its source to drain voltae drops with increasin common mode voltae V V V V V I, max dd 3 t M will o into triode when the drain voltae exceeds the ate voltae by more than Vt V I,min V6 + V tn V tp 7