IN3170/4170, Spring 2020 Philipp Häfliger hafliger@ifi.uio.no Excerpt of Sedra/Smith Chapter 7: Integrated CMOS Amplifier Basics
Content Thevenin and Norton Equivalent (book 1.1) Small Signal Analysis and Transistor Model (book 6.2) CMOS Common Source Amplifiers and FET Intrinsic Gain(book 7.3) Improved Current Mirrors/Sources (book 7.6)
Content Thevenin and Norton Equivalent (book 1.1) Small Signal Analysis and Transistor Model (book 6.2) CMOS Common Source Amplifiers and FET Intrinsic Gain(book 7.3) Improved Current Mirrors/Sources (book 7.6)
Thévenin and Norton (1/3) Two equivalent models of signal sources (e.g. a sensor or other transducer ): a) is called the The Thévenin form and b) the Norton form. Note: Outputresistance R S is the same in both models while v S ( t ) = i S ( t ) R S . A more general model would consider an output impedance , i.e. including output capacitance/inductance rather than just a resistance.
Thévenin and Norton (2/3) In general any circuit of linear components can be expressed as Thévenin or Norton equivalent circuit between two nodes of the circuit, with an equivalent resitance R S (or impedance Z S ) and (optionally) a signal or DC source. One often talks about the ’impedance seen in this node’ where the second node implicitly is Gnd.
Thévenin and Norton (3/3) To get the resistance in this node supply a test current i X or test voltage v X between the nodes and measure/compute the voltage or current respectively. R S is then δ v X δ i X . To get the signal source, for the Thevenin equivalent, measure/compute the output voltage (voltage-signal) for open circuit between the two terminals and for the Norton form, measure/compute the current (or current-signal) for a short circuit between the terminals. The Thevenin can be transformed into the Norton form or vice versa by using v S ( t ) = R S i S ( t ) .
Content Thevenin and Norton Equivalent (book 1.1) Small Signal Analysis and Transistor Model (book 6.2) CMOS Common Source Amplifiers and FET Intrinsic Gain(book 7.3) Improved Current Mirrors/Sources (book 7.6)
Intermezzo: Signal Naming Convention in the Book The book uses lower case letters with upper case indices to denominate large signal variables, i.e. with both DC (point of operation) and AC components. Upper case letters with upper case indices are just the DC components (point of operation) and lower case letters with lower case indices are small signal components. The latter is equivalent to the AC component for completely linear (!) systems. So for example: i D ≈ I D + i d
Small Signal Analysis i D ( v GS ) Equivalent to a 1 st order Taylor expansion, the small signals only model a linear approximation around a point of operation. Thus: di D i D ( v GS ) ≈ i D ( V GS ) + ( v GS − V GS ) ∗ dv GS � �� � � �� � � �� � I D v gs did dvgs = g m For strong inversion, active region: g m = di D = k n V OV dv GS Note: The DC component (i.e. point of operation) I D is ignored for small signal analysis, and simply defined to be zero.
Small Signal Analysis i D ( v DS ) Again a 1 st order Taylor expansion, i.e. a linear approximation around a point of operation: di D i D ( v DS ) ≈ i D ( V DS ) + ( v DS − V DS ) ∗ −4 8 x 10 dv DS � �� � � �� � 6 � �� � v ds 4 I D I D 2 did dvgs = 1 0 ro −2 0 0.5 1 1.5 2 2.5 3 3.5 V GS −5 3 x 10 For strong inversion, active region: 2 I D 1 r o = dv DS 1 = V A 0 = (5.26/27) 0 0.5 1 1.5 2 2.5 3 3.5 V DS di D λ I ′ I ′ D D Note that V A is proportional to transistor length L and thus sometimes expressed as V A = V ′ A L .
MOSFET Small Signal Circuit Model low frequency variant, i.e. neglecting capacitors
Applying the Small Signal Equivalent Circuits 1. Set all constant voltage sources (including DC biases) to Gnd 2. Set all constant current sources (including DC biases) to zero/open circuit 3. Substitute transistors with small signal equivalent circuit
Example: Common Source Amplifier A = g m ( R D || r o ) R O = R D || r o
Content Thevenin and Norton Equivalent (book 1.1) Small Signal Analysis and Transistor Model (book 6.2) CMOS Common Source Amplifiers and FET Intrinsic Gain(book 7.3) Improved Current Mirrors/Sources (book 7.6)
Intrinsic Gain from Small Signal
Intrinsic Gain vs Bias Current
CS Amplifier with Current-Source Load
CS Amplifier Analysis
CS with source degeneration no R L Good as current source, e.g in current mirror, but not so good as amplifier. R O ≈ ( 1 + g m R S ) r o g m g m → g ′ m = 1 + g m R s Much higher output resistance. Still no net-increase in gain!
CS with source degeneration with R L R L g ′ A v = m R O R L + R O R L ≈ g m r o R L + ( 1 + g m R S ) r o ... and more degradation to A v due to load R L !
Cascode Amplifier Can be looked upon as a CS and CG in series resulting in a intrinsic combined gain A = g m 1 r o 1 g m 2 r o 2 (i.e. with a large load resistance), or a circuit where the CS serves as high quality voltage controlled current source delivering i d ≈ g m 1 v i and the CG buffers that current to a high output resistance ≈ g m 2 r o 2 r o 1 .
Cascode Amplifier with Infinite Load Resistance
Folded Cascode with Infinite Load Resistance
Cascode Amplifier with Finite Load Resistance (1/2) The load R L must be of equal magnitude as R O to get the benefit of the increased gain A V ! So here with a simple pFET we are back to square one.
Cascode Amplifier with Finite Load Resistance (2/2) Better: employ a cascoded current source.
Dependency of Gain on R L
Content Thevenin and Norton Equivalent (book 1.1) Small Signal Analysis and Transistor Model (book 6.2) CMOS Common Source Amplifiers and FET Intrinsic Gain(book 7.3) Improved Current Mirrors/Sources (book 7.6)
Cascode Current Mirror Increased output impedance, but quite a bit of output voltage headroom necessary ...
Modified Wilson MOS Current Mirror
A CD-CS Amplifier Larger bandwidth than simple CS amplifier (explained later in chapter 9).
Recommend
More recommend
