ECE 5790 Spring 2014

Assignment #3

Hamidreza Aghasi

Optional submission: Friday, March 22, 2014

Mandatory submission: Friday, March 29 , 2014

Problem 5 is the extra problem for those who target the mandatory submission due date. Good Luck!

Contents

Problem 1: Folded Cascode LNA (30 points) 2

Problem 2: A1dB of highly nonlinear systems (20 points) 2

Problem 3: Linearity of Differential Pair(50 points) 3

Problem 4: Low Noise Amplifier Design (85 points) 3

Problem 5: Noise Figure in multi-transistor circuits(20 points) 5

1

Problem 1: Folded Cascode LNA (30 points)

The LNA shown in Fig.1 is designed to operate with low supply voltages. Each inductor is chosen to resonate

with the total capacitance at its corresponding node at the frequency of interest. Neglect channel-length

modulation and body effect and the noise due to the loss in L2(You need to model this loss components as a

prallel resistance of RP2 for calculating the gain and Noise Figure, but do not count the corresponding noise).

a)Determine the noise figure of the LNA with respect to a source resistance RS assuming that L1 can

be viewed as a resistance equal to Rp1 at the resonance frequency. Make sure the result reduces to a familiar

form if Rp .(Hint:the equivalent transconductance of a degenerated common-source stage is given bygm/(1 + gmR1),where R1 denotes the degeneration resistance.)(10 points)

b) Using BICMOS6hp process and your own values, simulate this circuit to achieve a noise figure smaller

than 4dB at 2.4 GHz frequency. Make sure that the circuit achieves this noise figure for a BW of larger

than 16 MHz. The total power consumption should be less than 10 mW and the inductors should have a

quality factor of 20. This design is good enough for an IEEE 802.11.a standard requirement. For this design

question please submit your clear plots/figures showing the performance for each specification.(20 points)

Figure 1: Folded Cascode LNA

Problem 2: A1dB of highly nonlinear systems (20 points)

Under certain conditions, we could model a nonlinear system by:

y(t) = 1x(t) + 2x2(t) + 3x

3(t) + 4x4(t) + 5x

5(t) (1)

As we saw in class, for a weakly nonlinear circuit, the 1-dB compression point can be calculated as

A1dB =

0.145|13| (2)

This equation fails to explain the measured 1-dB compression point of highly nonlinear systems. In this

case, we should take into account higher order nonlinear coefficients. With similar technique that we used

to obtain eqn.(2), find the 1-dB compression point of a system with nonlinear coefficients up to fifth order.

Page 2 of 5

Problem 2: A1dB of highly nonlinear systems (20 points)

Problem 3: Linearity of Differential Pair(50 points)

In this problem, we are going to compare the linearity of bipolar amplifiers in different structures. Lets first

assume we have a common emitter amplifier as shown in figure 2.

a)Calculate the 1-dB compression point of the amplifier shown in figure 2.(3rd order nonlinearity)(5 points)

b) How does the linearity change when we make a differential pair as shown in figure 3?(Assume that

only three nonlinear coefficients are enough to characterize the behavior of the amplifier. Also if you need

any numerical value for the parameters in the problem, assume some typical values!)(10 points)

c)(Bonus) What is the IIP3 of the circuit shown in figure 3? To do so, similar to our calculation in class,

assume a two tone input and find out the gain of fundamental and third-order intermodulation products and

set them equal.(10 points)

d)(Bonus) To further enhance the linearity, you design the structure shown in figure 4. For this circuit what

should be the value of Ibias, in order that the amplifier has the same transconductance as a conventional

differential pair with a tail current of IEE? (10 points)

e) (Bonus) What is the 1-dB compression point of the circuit in figure 4?(10 points)

f) (Bonus) What is the IIP3 of the circuit shown in figure 4?(5 points)

Figure 2: simple bipolar amplifier

Problem 4: Low Noise Amplifier Design (85 points)

In our class discussions, we saw that the Bipolar transistor exhibits a very nonlinear performance which

makes it hard to design an LNA. In last question, we also compared the nonlinearity of a single-ended am-

plifier and a differential amplifier. In this problem we are going to design a very good Low Noise Amplifier

using the BiCMOS6hp process. I should mention that if you had met these specifications a few years ago,

you had a very famous paper on LNA design. For this design we are going to use the structure shown in

figure 5.

Before starting the design, lets first review a few circuit problems.

Problem 4: Low Noise Amplifier Design (85 points) continued on next page. . . Page 3 of 5

Problem 4: Low Noise Amplifier Design (85 points) (continued)

Figure 3: Bipolar Differential pair

Figure 4: Modified Bipolar Differential pair

a) What is the small signal gain of the circuit shown in figure 5, neglecting the channel length modula-

tion and body effect? For this part assume that each transistor is biased with a current of 5mA and all the

transistors are biased 200 mV above the Threshold voltage.(In this part we assume zero coupling between

inductors)(10 points)

b) The combination of L1 and C1 is for the sake of segregation between the bias and RF signal. As-

suming that for the matching, we have a direct connection from the input source to transistor, find the

values of Ls, Cf and Lg to have S11 < 20 dB at 3 GHz.(5 points)

c) Compute the NF of each branch, assuming lossless passive components and neglecting the flicker noise of

transistors.(10 points)

d)(Bonus) Assume that there exists a non-zero coupling between the drain inductors. Find the small

signal gain in terms of the coupling coefficient.(10 points)

Problem 4: Low Noise Amplifier Design (85 points) continued on next page. . . Page 4 of 5

Problem 4: Low Noise Amplifier Design (85 points) (continued)

Figure 5: Proposed structure

e)In this part, we are going to design an LNA(With new bias conditions of your choice), using this structure

with the following specifications:

Gain ' 9dB NFmin < 4dB 3dB-Bandwidth from 2.5 4 GHz Power consumption < 20 mW S11,min < 13dB S12 < 5dB throughout the 3-dB BW IIP3 > 2dBm Quality factor of inductors =20 (Use the library capacitor models)

Your final grade from part e is calculated from the following formula:

Grade = 50 (9Gain) (4NF ) (Power 20)2

(S11 + 13)1.5

(S12 + 5) (2 IIP3) (3)

For this design question please submit your clear plots/figures showing the performance for each specification.

Problem 5: Noise Figure in multi-transistor circuits(20 points)

Determine the Noise Figure of circuits in figure 2.79 (a and e) of the textbook with respect to a source

impedance of Rs. Neglect the channel length modulation and body effect.

Page 5 of 5

Problem 1: Folded Cascode LNA (30 points)Problem 2: A1-dB of highly nonlinear systems (20 points)Problem 3: Linearity of Differential Pair(50 points)Problem 4: Low Noise Amplifier Design (85 points)Problem 5: Noise Figure in multi-transistor circuits(20 points)