Short-Circuit Transconductance and Voltage Gain in Cascode Stages
"Learn about the importance of short-circuit transconductance in circuit strength, the derivation of voltage gain, comparison between bipolar cascode and CE stages, and practical considerations for improved cascode stages."
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Presentation Transcript
Short-Circuit Transconductance i = out v G m in = 0 v out The short-circuit transconductance of a circuit measures its strength in converting input voltage to output current. CH 9 Cascode Stages and Current Mirrors 2
Transconductance Example G = g 1 m m CH 9 Cascode Stages and Current Mirrors 3
Derivation of Voltage Gain = = v i R G v R out out = out G m in out v v R out in m out By representing a linear circuit with its Norton equivalent, the relationship between Vout and Vin can be expressed by the product of Gm and Rout. CH 9 Cascode Stages and Current Mirrors 4
Example: Voltage Gain = A g 1 O m r 1 v CH 9 Cascode Stages and Current Mirrors 5
Comparison between Bipolar Cascode and CE Stage Since the output impedance of bipolar cascode is higher than that of the CE stage, we would expect its voltage gain to be higher as well. CH 9 Cascode Stages and Current Mirrors 6
Voltage Gain of Bipolar Cascode Amplifier G g 1 m m ( || ) A g r g r r 1 1 1 2 v m O m O 1 Since rO is much larger than 1/gm, most of IC,Q1 flows into the diode-connected Q2. Using Rout as before, AV is easily calculated. CH 9 Cascode Stages and Current Mirrors 7
Alternate View of Cascode Amplifier A bipolar cascode amplifier is also a CE stage in series with a CB stage. CH 9 Cascode Stages and Current Mirrors 8
Practical Cascode Stage out || ( || ) R r g r r r 3 2 2 1 2 O m O O Since no current source can be ideal, the output impedance drops. CH 9 Cascode Stages and Current Mirrors 9
Improved Cascode Stage out ( || || ) 3 r ( || ) R g r r g r r r 3 3 4 2 2 1 2 m O O m O O In order to preserve the high output impedance, a cascode PNP current source is used. CH 9 Cascode Stages and Current Mirrors 10
MOS Cascode Amplifier = A G R v m out 1 ( r + + ) A g g r r r 1 2 2 1 2 v m m r O O O A g g 1 1 2 2 v m O m O CH 9 Cascode Stages and Current Mirrors 11
Improved MOS Cascode Amplifier R g r r 2 2 1 on m O O R g r r 3 3 4 op m O || O = R R R out on op Similar to its bipolar counterpart, the output impedance of a MOS cascode amplifier can be improved by using a PMOS cascode current source. CH 9 Cascode Stages and Current Mirrors 12
Temperature and Supply Dependence of Bias Current + = ( ) ln( ) R V R R V I I 2 1 2 1 CC T S 2 R 1 W = 2 I C V V 1 n ox DD TH + 2 L R R 1 2 Since VT, IS, n, and VTHall depend on temperature, I1 for both bipolar and MOS depends on temperature and supply. CH 9 Cascode Stages and Current Mirrors 13
Concept of Current Mirror The motivation behind a current mirror is to sense the current from a golden current source and duplicate this golden current to other locations. CH 9 Cascode Stages and Current Mirrors 14
Bipolar Current Mirror Circuitry I = 1 S I I copy REF I , S REF The diode-connected QREFproduces an output voltage V1 that forces Icopy1 = IREF, if Q1 = QREF. CH 9 Cascode Stages and Current Mirrors 15
Bad Current Mirror Example I Without shorting the collector and base of QREF together, there will not be a path for the base currents to flow, therefore, Icopy is zero. CH 9 Cascode Stages and Current Mirrors 16
Bad Current Mirror Example II Although a path for base currents exists, this technique of biasing is no better than resistive divider. CH 9 Cascode Stages and Current Mirrors 17
Multiple Copies of IREF I , S j ,= I I copy j REF I , S REF Multiple copies of IREFcan be generated at different locations by simply applying the idea of current mirror to more transistors. CH 9 Cascode Stages and Current Mirrors 18
