Analog Electronic Circuits

(1)

Department of Electrical and Computer Engineering Seoul National University

2020 Fall D.K. Jeong

Homework Assignments #6 - Due: 2020/12/23

- There will be a 15-min. quiz on the homework questions before lecture.

1. Solve textbook problems in Chapter 14: 2, 19, 21, 25, and 37.

14.2

14.19

(2)

14.21

(3)

14.25

14.37

(4)

2. Consider the following circuit shown in Fig. 1. Assume that VCC = 15V, VEE = -15V, VT = 26mV, IS,Q1 = IS,Q4 = 10^-14A, IS,Q2 = IS,Q3 = 10^-13A, and VA =∞. Also assume that the output is sinusoidal with maximum amplitude of 12V (i.e. VOUT =12sinωt).

R

₁

=2kΩ R

2

V

CC

V

EE

I

BIAS

V

IN

V

OUT

R

_L

=8Ω Q

₁

Q

₂

Q

3

Q

₄

V

X

Fig. 1

(a) Calculate VX using R1, R2, and VBE1. Assume that βQ1=∞.

R1

R2

I

R

I

C1

V

X VBE1

𝑉_𝑋= (𝑅₁+ 𝑅₂)𝐼_𝑅 - (1) 𝑉𝐵𝐸1= 𝑅1𝐼𝑅 - (2)

 𝑉_𝑋= (1 +^𝑅²

𝑅₁) 𝑉_𝐵𝐸1

(5)

(b) Calculate the minimum value of the bias current, IBIAS. Assume that βQ2=βQ3=100.

𝑉_𝑂𝑈𝑇 = 12𝑉 일 때 𝐼_𝐵3 가 최대이므로, 이 때 𝐼_𝐵,𝑄3≤ 𝐼_{𝐵𝐼𝐴𝑆} 조건을 만족시켜야 함.

 𝐼𝐶,𝑄3 =^12𝑉

8Ω = (β + 1)𝐼𝐵,𝑄3

 𝐼_𝐵,𝑄3≈ 15𝑚𝐴

∴ 𝐼_{𝐵𝐼𝐴𝑆} ≥ 15𝑚𝐴  𝐼_{𝐵𝐼𝐴𝑆,𝑚𝑖𝑛} = 15𝑚𝐴

(c) Using the value of (b), find the value of R2 to set the quiescent current at the output transistors to 20mA. (Quiescent current condition : VOUT=0)

R1

R2

VCC

VEE IBIAS=15mA

VIN

0V Q1

Q2

Q3

Q4

VX

I=20mA (IC≈ IE) IB,Q3=0.2mA

IR

IC,Q1

𝑉𝑋= 𝑉𝐵𝐸3+ 𝑉𝐸𝐵2= 𝑉𝑇𝑙𝑛^𝐼^𝐶,𝑄3

𝐼_𝑆,𝑄3+ 𝑉𝑇𝑙𝑛^𝐼^𝐶,𝑄2

𝐼_𝑆,𝑄2= 2 × 26mV × ln ^20𝑚𝐴

10⁻¹³𝐴= 1.353𝑉 – (3) 𝑉𝐵𝐸1= 𝑉𝑇𝑙𝑛^𝐼^𝐶,𝑄1

𝐼_𝑆,𝑄1= 26mV × ln15𝑚𝐴−200𝑢𝐴−𝐼_𝑅

10⁻¹⁴𝐴 = 2𝑘Ω × 𝐼𝑅  𝐼𝑅 ≈ 364𝑢𝐴 – (4) (3), (4)에 의해 𝑉_𝑋 = (𝑅₁+ 𝑅₂)𝐼_𝑅  1.353𝑉 = (2000 + 𝑅₂)364𝑢𝐴

∴ 𝑅₂≈ 1.72𝑘Ω

(d) What is the power efficiency? Ignore the power dissipation at the pre-driver.

η = ^𝑃^𝑂𝑈𝑇

𝑃_𝑂𝑈𝑇+𝑃_{𝑎𝑣,𝑄2}+𝑃_{𝑎𝑣,𝑄3}=^𝜋

4 𝑉_𝑃 𝑉_𝐶𝐶=^𝜋

4 12

15= 0.628

∴ 𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 = 62.8%