1. VDD
VDD
VDD
- +
Vref R xR Q nQ nQ

2. Cascoded CM
Cascoded CG
amplifier
Make x*ln(n)26
Can change M7-M10 to wide swing cascode connections to accommodate lower supply voltages.

3. Chapter 7 Figure 15
Polarity is wrong.

4. Banba, Hironori, Hitoshi Shiga, Akira Umezawa, Takeshi Miyaba, Toru Tanzawa, Shigeru Atsumi, and Koji Sakui. "A CMOS bandgap reference circuit with sub-1-V operation." Solid-State Circuits, IEEE Journal of 34, no. 5 (1999):

6. Noise in time domain

7. dBm is a unit used to measure physical power relative to 1 mW.
For exampl, if 2V is applied to 50, the physical power is:
P= 2^2/50 W = 4/50 W = 4*20 mW
P (dDm) = 10log(P/1mW) = 10log(80) = 10log(2^3*10) = 3* =19.03 dBm

8. Area For a given v(t), define: vf(t) v(t)
The power spectral density of v is:
Pv(f) = power of vf(t) = power of v(t) in a one Hertz bandwidth at f
The total power of v can be obtained by integrating Pv(f) over all f.
Pv(f)
Pv = 10*1M + 0.5*10*1M
= 15M (uV)2=15(mV)2
10(uV)2/Hz
Area
1MHz
2MHz

9. If the power spectral density of vn is flat (ind of f), vn is called white.
vn(t)
Pvn(f)

10. dBm or dBV2
Slope: 10dB/dec
log(f)

11. 1/f noise corner: the intersection of 1/f noise power spectral density and white noise power spectral density
dBm or dBV2
Slope: 10dB/dec
1/f noise corner
log(f)

12. Filtered noise:
Time domain
spectrum

13. -20dB/dec

14. Filtered noise:
Chapter 9 Figure 06
Chapter 9 Figure 07

15. R1 R2 R3 Vo +-
VDC