hw7.ee140-240a.f15.v5 - University of California, Berkeley€¦ · · 2015-10-23Microsoft Word -...
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EE 140 / EE 240A ANALOG INTEGRATED CIRCUITS FALL 2015 C. Nguyen PROBLEM SET #7 Issued: Friday, Oct. 16, 2015 Due (at 8 a.m.): Monday, Oct. 26, 2015, in the EE 140/240A HW box near 125 Cory. 1. A design error has resulted in a mismatch in the circuit of Fig. PS7-1. Specifically, ! has twice the / ratiio of ! . If !" is a small sine-wave signal, find an expression for (a) !! and !! . (b) !" for each of ! and ! . (c) The differential gain !! in terms of ! , , and !" . Fig. PS7-1 V DD M 1 M 2
Transcript of hw7.ee140-240a.f15.v5 - University of California, Berkeley€¦ · · 2015-10-23Microsoft Word -...
EE 140 / EE 240A ANALOG INTEGRATED CIRCUITS FALL 2015 C. Nguyen
PROBLEM SET #7
Issued: Friday, Oct. 16, 2015
Due (at 8 a.m.): Monday, Oct. 26, 2015, in the EE 140/240A HW box near 125 Cory.
1. A design error has resulted in a mismatch in the circuit of Fig. PS7-1. Specifically, 𝑀! has twice the 𝑊/𝐿 ratiio of 𝑀!. If 𝑉!" is a small sine-wave signal, find an expression for
(a) 𝐼!! and 𝐼!!.
(b) 𝑉!" for each of 𝑀! and 𝑀!.
(c) The differential gain 𝐴!! in terms of 𝑅!, 𝐼, and 𝑉!".
Fig. PS7-1
VDD
M1 M2
EE 140 / EE 240A ANALOG INTEGRATED CIRCUITS FALL 2015 C. Nguyen
2. The differential amplifier in Fig. PS7-2 utilizes a resistor 𝑅!! to esiablish a 1-mA dc bias
current. Note that this amplifier uses a single 5-V supply and thus needs a dc common-mode voltage 𝑉!". Transistors 𝑀! and 𝑀! have 𝑘!𝑊/𝐿= 2.5mA/V2, 𝑉!=0.7V, and 𝜆=0.
(a) Find the required value of 𝑉!".
(b) Find the value of 𝑅! that results in a differential gain 𝐴!! of 8 V/V.
(c) Determine the dc voltage at the drains
(d) Determine the common-mode gain 𝑣!/𝑣!" and CMRR for this amplifier. (Hint: You need to take 1/gm into account.)
(e) Use the common-mode gain found in (d) to determine the change in 𝑉!" that results in 𝑀! and 𝑀! entering the triode region.
Fig. PS7-2
VD1 VD2 M1 M2
EE 140 / EE 240A ANALOG INTEGRATED CIRCUITS FALL 2015 C. Nguyen
3. Fig. PS7-3 shows a high-gain op amp design with cascade devices. Let 𝐼!! = 1mA, 𝑉!! = 3V,
𝑉!! = 1.7V and 𝑉!! = 1.6V. Assuming 𝛾 = 0 and 𝑉!",!"" =0.2V , find the mid-band gain 𝑣!"#/𝑣!", input common-mode range, and the output swing.
MOS Parameters:
𝜇!𝐶!" =135µAV! , 𝜇!𝐶!" =
38µAV! 𝑉!" = 0.7 V,𝑉!" = −0.8 V, 𝜆! = 𝜆! = 0.1,
𝑊𝐿 !,!,!,!
=100µm0.34µm ,
𝑊𝐿 !,!,!,!
=100µm0.32µm
Fig. PS7-3
VB2
VB1
+
-
EE 140 / EE 240A ANALOG INTEGRATED CIRCUITS FALL 2015 C. Nguyen
4. Fig. PS7-4 shows a two-stage CMOS op amp. Let 𝐼!"# = 90µA, 𝑉!! = 𝑉!! = 2.5𝑉, and 𝐶! = 0. Find the mid-band gain 𝑣!/(𝑣! − 𝑣!), input common-mode range, and the output swing.
MOS Parameters:
𝜇!𝐶!" =160µAV! , 𝜇!𝐶!" =
40µAV! ,𝑉!" = 0.7 V,𝑉!" = −0.8 V, 𝜆! = 𝜆! = 0.1,
!! !,!
= !"!!!.!!!
, !! !,!
= !"!!.!!!
, !! !,!,!
= !"#!!.!!!
, !! !
= !"#!!.!!!
Fig. PS7-4
v+ v$
VDD
-VSS
M8 M5 M7
M1 M2
M3 M4 M6
EE 140 / EE 240A ANALOG INTEGRATED CIRCUITS FALL 2015 C. Nguyen
5. Fig. PS7-5 shows a multi-stage BJT OPAmp design. BJTs 𝑄! − 𝑄! have the same size
except for 𝑄!, which is 4x larger than 𝑄!. Ignore Early effect.
(a) Assuming 𝛽 ≫ 1 and 𝑉!" = 0.7𝑉, calculate the DC currents flowing through 𝑄! − 𝑄!.
(b) Calculate the static power dissipation of this op amp.
(c) If transistors 𝑄! and 𝑄! have 𝛽 = 100, what is the input bias current of this op amp?
(d) If 𝑉!"(!"#) = 0.4V, determine the input common-mode range of this op amp.
(e) Calculate the input resistance, mid-band gain 𝑣!/𝑣!", and the output resistance of this op amp.
Fig. PS7-5
+15V
-15V
+15V
