Lecture 7a
EE-215 Electronic Devices and Circuits
Dr. Muhammad Anis Chaudhary
Small-Signal Operation and Models
Small-Signal Equivalent Circuit Models
• we had already seen the small-signal equivalent circuit model (hybrid-π model) for an NMOS
transistor
Small-Signal Operation and Models
Small-Signal Equivalent Circuit Models
• also for PMOS transistor, the MOSFET acts as a voltage controlled current source.
• thus the small-signal model for the p-channel MOSFET can be given as
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Small-Signal Operation and Models
Small-Signal Equivalent Circuit Models
• In the small-signal model of PMOS transistor,
– if we substitute, vsg = −vgs
– =⇒ gm vsg = −gm vgs
– i.e. if the control voltage polarity is reversed, then the dependent current direction is also
reversed.
• also vsd = −vds
Small-Signal Operation and Models
Small-Signal Equivalent Circuit Models
• thus the resultant equivalent circuit (fig b) for the PMOS transistor is exactly the same as that
of the NMOS transistor
• we conclude that the small-signal equivalent circuit model (hybrid-π model) is
– exactly the same for both the NMOS and the PMOS transistors
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Small-Signal Operation and Models
The T Equivalent-Circuit Model
Small-Signal Operation and Models
The T Equivalent-Circuit Model
• A simple circuit transformation can lead to an alternative
– equivalent circuit model for a MOSFET
• we start with the hybrid-π model
• here we have placed a 2nd gm vgs current source in series with the original controlled source.
• Note that, this new current source doesnot change the terminal currents and is thus allowed
Small-Signal Operation and Models
The T Equivalent-Circuit Model
• the new node X, can be connected to the gate.
• As because of KCL, still the gate current ig = 0 .
• so the gate current is still zero (i.e. this connection doesnot change the terminal characteristics)
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Small-Signal Operation and Models
The T Equivalent-Circuit Model
• Note that, here we have a controlled current source gm vgs
– whose current is controlled by the control voltage vgs
– where vgs is across itself
vgs 1
• =⇒ this current source can be replaced by a resistor of value gm vgs = gm
Small-Signal Operation and Models
The T Equivalent-Circuit Model
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• Note that the resistance between the gate and the source,
– looking in to the source terminal is 1/gm
– and looking in to the gate terminal is infinite
Small-Signal Operation and Models
The T Equivalent-Circuit Model
• if the channel-length modulation effect cannot be ignored,
– we can include ro in the T-model between the drain and the source terminal
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Small-Signal Operation and Models
The T Equivalent-Circuit Model
• Also we can have an alternative representation of the T model,
– where we can replace the voltage-controlled current source by
– a current controlled current source
Small-Signal Operation and Models
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Small-Signal Operation and Models
Example 5.11
• Figure 5.42(a) shows a MOSFET amplifier biased by a constant-current source I. Assume
that the values of I and RD are such that the MOSFET operates in the saturation region. The
input signal vi is coupled to the source terminal by utilizing a large capacitor CC1 . Similarly,
the output signal at the drain is taken through a large coupling capacitor CC2 . Find the input
resistance Rin and the voltage gain vo ⁄vi . Neglect channel-length modulation.
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Small-Signal Operation and Models
Example 5.11
vo
• here λ = 0 , Rin =? , Av = vi =?
• as an ac source is connected at the source terminal of the MOSFET, it is more convenient to use
T-model.
• thus for ac analysis,
– suppress dc sources i.e. VDD is replaced by short circuit
* and I is replaced by an open circuit
– CC1 , CC2 are replaced by short circuits
– MOSFET is replaced by its T-model
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Small-Signal Operation and Models
Example 5.11
Small-Signal Operation and Models
Example 5.11
vgs 1
• as i = gm and vgs = −vi
−vi 1
– =⇒ i = gm
vi vi −vi 1
• and Rin = ii = −i = i = gm
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• by ohm’s law at RD
– vo = (−i) RD
vgs
– As i = 1/gm = gm vgs
• =⇒ vo = −gm vgs RD
• or vo = −gm (−vi ) RD ∵vgs = −vi
vo
• vo = gm vi RD =⇒ Av = vi = gm RD
Basic MOSFET Amplifier Configurations
Basic MOSFET Amplifier Configurations
Basic MOSFET Amplifier Configurations
Basic MOSFET Amplifier Configurations
• we have already determined that
– almost-linear amplification can be obtained by
– biasing the MOSFET at a suitable point Q in
– its saturation region of operation
– and by keeping the signal vgs small
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Basic MOSFET Amplifier Configurations
Basic MOSFET Amplifier Configurations
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Basic MOSFET Amplifier Configurations
• Also when vgs is small, the MOSFET can be replaced by its small-signal circuit model (either
hybrid-π model or the T-model)
• the resultant ac circuit can be used to determine the amplifier parameters like
– the voltage gain,
– the input resistance
– and the output resistance
Basic MOSFET Amplifier Configurations
Basic MOSFET Amplifier Configurations
The Three Basic Configurations
Basic MOSFET Amplifier Configurations
The Three Basic Configurations
• There are three basic configurations for connecting the MOSFET as an amplifier, namely
– the Common Source (CS) Amplifier
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– the Common Gate (CG) Amplifier
– The Common Drain (CD) Amplifier (also called Source Follower)
• Each of these configurations is obtained by
– connecting one of the three MOSFET terminals to ground
– thus creating a two-port network with the grounded terminal
– being common to the input and output ports
• The resulting three configurations with biasing arrangement ommited are shown in fig
Basic MOSFET Amplifier Configurations
Basic MOSFET Amplifier Configurations
The Three Basic Configurations
Common Source Amplifier
• here the source terminal is connected to ground,
• the input voltage is applied at the gate (w.r.t ground),
• the output voltage is taken at the drain (w.r.t ground)
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• this configuration is called the grounded source or the common source (CS) amplifier
• Note that dc biasing circuit is not shown in figure
Basic MOSFET Amplifier Configurations
The Three Basic Configurations
Common Gate Amplifier
• The common gate (CG) or grounded gate amplifier is obtained
• by connecting the gate to ground,
• applying the input between the source and ground
• taking the output vo between the drain and ground
• Note that dc biasing circuit is not shown in figure
Basic MOSFET Amplifier Configurations
The Three Basic Configurations
Common Drain Amplifier
• The common drain (CD) or grounded drain amplifier is obtained
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• by connecting the drain terminal to ground,
• applying the input between the gate and ground
• taking the output vo between the source and ground
• Note that dc biasing circuit is not shown in figure
• the Common Drain amplifier is also called Source Follower
Basic MOSFET Amplifier Configurations
Characterizing Amplifiers
Basic MOSFET Amplifier Configurations
Characterizing Amplifiers
• lets take a look at how to characterize the performance of an amplifier as a circuit building block
• here an amplifier is fed with a signal source
– having an open-circuit voltage vsig and an internal resistance Rsig
• this voltage source (vsig , Rsig ) can be an actual signal source
– or in a cascade amplifier, it can be the Thevenin equivalent of the output circuit of the
preceeding amplifier.
• the load resistor RL is connected at the output terminal of the amplifier
– this RL can be an actual load resistor
– or the input resistance of a succeeding amplifier stage in a cascade amplifier
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Basic MOSFET Amplifier Configurations
Characterizing Amplifiers
• The amplfier block can be replaced by its equivalent circuit model
• the input resistance Rin
– indicate the loading effect of the amplifier input on the signal source
vi
– and is given as Rin = ii
• by voltage divider rule
Rin
– vi = Rin +Rsig vsig
Basic MOSFET Amplifier Configurations
Characterizing Amplifiers
Rin
• vi = Rin +Rsig vsig
• Avo is the open-circuit voltage gain and is defined as
vo
– Avo = vi R =∞
L
Basic MOSFET Amplifier Configurations
Characterizing Amplifiers
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• the 3rd parameter that is essential to characterize an amplifier is the output resistance Ro
– Ro is the resistance seen looking back into the amplfier output terminal with vi set to zero
vx
– =⇒ Ro = ix
• Note that the controlled source Avo vi and the output resistance Ro
– represent the Thevenin equivalent of the amplifier output circuit.
Basic MOSFET Amplifier Configurations
Characterizing Amplifiers
• by voltage divider
– the output voltage vo can be given as
RL
– vo = RL +Ro (Avo vi ) =⇒ vo
vi = Avo RLR+R
L
o
• thus the voltage gain of the amplifier is
– Av = vo
vi = Avo RLR+R
L
o
• the overall voltage gain is
vi
– Gv = vo
vsig = Avo RLR+R
L
o vsig
Rin Rin
– Gv = Avo RLR+R
L
o Rin +Rsig
∵vi = Rin +Rsig vsig
Basic MOSFET Amplifier Configurations
The Common-Source (CS) Amplifier
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