# Recitation 21: Intrinsic Frequency Response of CS &amp; CE Ampliﬁer

```Recitation 21
Intrinsic Frequency Response of CS &amp; CE Ampliﬁer 6.012 Spring 2009
Recitation 21: Intrinsic Frequency Response of CS
&amp; CE Ampliﬁer
Yesterday, we discussed the intrinsic frequency response of the CE Ampliﬁer. Since there is
an analogy between MOSFET &amp; BJT, today we will look at the intrinsic frequency response
of a CS Ampliﬁer and compare them.
Small Signal Model
MOSFET
BJT
VSB = 0: so only 3 terminals
BJT
Cπ = Cje + Cb = Cje + gm τF = Cje + gm
Cμ :
MOSFET
2
wB
2D n
Cgs = 23 wLCox + wCov
Cgd = wCov
depletion capacitance only
1
Recitation 21
Intrinsic Frequency Response of CS &amp; CE Ampliﬁer 6.012 Spring 2009
Intrinsic Frequency Response: Rs → ∞ RL = 0
BJT
Node 1: iin =
vπ
γπ
MOSFET
Node 1: iin = jwCgs &middot; Vgs + jwCgd Vgs
+ jwCπ &middot; vπ + jwCμ vπ
Node 2: iout = gm vπ − jwCμ vπ
jwCμ
g
γ
1
−
m
π
gm
iout
=
1 + jwγ
(C
iin
π π +C
μ )
jwCμ
βo 1 − gm
=
1 + jwγπ (Cπ + Cμ )
Node 2: iout = gm vπ − jw
iout
gm − jwCgd
=
jw(Cgs + Cgd )
iin
2
Recitation 21
Intrinsic Frequency Response of CS &amp; CE Ampliﬁer 6.012 Spring 2009
Unit Gain Frequency, fT
BJT
MOSFET
1
1
gm
wT =
2π
2π Cμ + Cπ
Frequency at which the current gain is reduced to
1(0 dB)
This is obtained by:
jwCμ
i βo 1 − g
out m
=
=1
iin
1 + jwγπ (Cμ + Cπ )
fT =
gm
ignoring the zero on top, ∵
wT
Cμ
βo
=1
1 + jwγπ (Cμ + Cπ )
∵ wT γπ (Cμ1+Cπ ) ∴ wT γπ (Cμ + Cπ ) 1
βo
gm
= 1 =⇒ wT =
jwγπ (Cμ + Cπ )
Cμ + Cπ
fT =
1
gm
2π Cgs + Cgd
(this can be derived similar to the BJT case)
fT =
Physical interpretation:
gm
2π(Cgs + Cgd )
1 gm
1 w/Lμn Cox (VGS − 1)
2π Cgs
2π
2/3wLCox
1 3 μn (VGS − VT )
3 μn VD,SAT 1
=
2
2π 2
2
L2
2π
L
μn VDSAT
∼ velocity of carrier
L
fT =
μn VDSAT
/L ∼ 1/τT = τT = L/ velocity
L
τT is transit time from source to drain
1 Ic /Vth
Ic
+ Cje + Cμ (∵ gm =
)
Vth
2π Ic /Vth &middot; τF
fT is independent of V .
For high frequency performance, NMOS &gt; PMOS.
Scale L as short as possible
3
Recitation 21
Intrinsic Frequency Response of CS &amp; CE Ampliﬁer 6.012 Spring 2009
At low Ic , fT is dominated by depletion capacitances at Base-emitter and base collector junctions (Cje and Cμ ). As Ic ↑, diﬀusion capacitance
gm τF ↑, and becomes dominant.
Fundamental limit for frequency response
2
wB
τF =
2Dn,p
To increase fT
- high Ic = diﬀusion cap. limited =⇒ shrink base
width.
- low Ic = depletion cap. limited =⇒ shrink
device area
4
Another note for MOSFET: the current gain → ∞ at w = 0.
This is because of gate oxide, DC input current = 0.
MOSFET not used as current ampliﬁer at low frequency
(input resistance too high)
MIT OpenCourseWare
http://ocw.mit.edu
6.012 Microelectronic Devices and Circuits
Spring 2009