[HW1 Solution] 1. V =1.8 V DD - Semiconductor System...

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[HW1 Solution] 1. R in = 1 βˆ₯ 2 β‰₯ 20Ξ© I DS = 1 2 οΏ½ 200Β΅A V 2 οΏ½ οΏ½ 20 0.18 οΏ½ ( βˆ’ ) 2 =1 V GS = 0.7, = 2 1 + 2 β‰₯ . , β‰₯ . 2. (a) R out R S v x , i x r O v gs g m v gs v gs = βˆ’ = βˆ’ , βˆ’ +g m = βˆ’ βˆ’ g m = = ={ +( + ) } V DD =1.8 V 500Ξ© M 1 R 1 R 2

Transcript of [HW1 Solution] 1. V =1.8 V DD - Semiconductor System...

Page 1: [HW1 Solution] 1. V =1.8 V DD - Semiconductor System Labssl.kaist.ac.kr/class/17spring/ee403/hw/HW1_sol.pdfΒ Β· Β Β· 2017-03-23[HW1 Solution] 1. 1. Rin= 𝑅𝑅1βˆ₯𝑅𝑅2β‰₯20π‘˜π‘˜Ξ©

[HW1 Solution]

1.

Rin = 𝑅𝑅1 βˆ₯ 𝑅𝑅2 β‰₯ 20π‘˜π‘˜Ξ©

IDS =12οΏ½

200Β΅AV2 οΏ½ οΏ½

200.18

οΏ½ (𝑉𝑉𝐺𝐺𝐺𝐺 βˆ’ 𝑉𝑉𝑑𝑑)2 = 1π‘šπ‘šπ‘šπ‘š

VGS = 0.7𝑉𝑉,𝑉𝑉𝐺𝐺𝐺𝐺 =𝑅𝑅2

𝑅𝑅1 + 𝑅𝑅2

π‘π‘πŸπŸ β‰₯ πŸ“πŸ“πŸπŸ.πŸ’πŸ’πŸ’πŸ’π›€π›€,π‘Ήπ‘ΉπŸπŸ β‰₯ πŸ‘πŸ‘πŸπŸ.πŸ•πŸ•πŸ•πŸ•π›€π›€

2.

(a) Rout

RS

vx, ixrOvgs gmvgs

vgs = βˆ’π‘–π‘–π‘₯π‘₯𝑅𝑅𝐺𝐺 = βˆ’π‘‰π‘‰π‘ π‘ ,𝑣𝑣π‘₯π‘₯ βˆ’ π‘‰π‘‰π‘ π‘ π‘Ÿπ‘Ÿπ‘œπ‘œ

+ gm𝑣𝑣𝑔𝑔𝑠𝑠 = 𝑖𝑖π‘₯π‘₯

𝑣𝑣π‘₯π‘₯ βˆ’ 𝑖𝑖π‘₯π‘₯π‘…π‘…πΊπΊπ‘Ÿπ‘Ÿπ‘œπ‘œ

βˆ’ gm𝑖𝑖π‘₯π‘₯𝑅𝑅𝐺𝐺 = 𝑖𝑖π‘₯π‘₯

𝐑𝐑𝐨𝐨𝐨𝐨𝐨𝐨 =π’—π’—π’™π’™π’Šπ’Šπ’™π’™

= {𝒓𝒓𝒐𝒐 + (𝟏𝟏 + π’ˆπ’ˆπ’Žπ’Žπ’“π’“π’π’)𝑹𝑹𝑺𝑺}

VDD=1.8 V

500Ξ©

M1

R1

R2

Page 2: [HW1 Solution] 1. V =1.8 V DD - Semiconductor System Labssl.kaist.ac.kr/class/17spring/ee403/hw/HW1_sol.pdfΒ Β· Β Β· 2017-03-23[HW1 Solution] 1. 1. Rin= 𝑅𝑅1βˆ₯𝑅𝑅2β‰₯20π‘˜π‘˜Ξ©

(b) Rin

rOvgs gmvgs

vx, ix

RL

vx = βˆ’π‘£π‘£π‘”π‘”π‘ π‘ , οΏ½ix + π‘”π‘”π‘šπ‘šπ‘£π‘£π‘”π‘”π‘ π‘ οΏ½ro + ix𝑅𝑅𝐿𝐿 = 𝑣𝑣π‘₯π‘₯

ix(π‘Ÿπ‘Ÿπ‘œπ‘œ + 𝑅𝑅𝐿𝐿) = 𝑣𝑣π‘₯π‘₯(1 + π‘”π‘”π‘šπ‘šπ‘Ÿπ‘Ÿπ‘œπ‘œ)

𝐑𝐑𝐒𝐒𝐒𝐒 =π’—π’—π’™π’™π’Šπ’Šπ’™π’™

=𝒓𝒓𝒐𝒐 + π‘Ήπ‘Ήπ‘³π‘³πŸπŸ + π’ˆπ’ˆπ’Žπ’Žπ’“π’“π’π’

3.

rOvin=vgs gmvgs

RD

RS voutix

ix = π‘”π‘”π‘šπ‘šπ‘£π‘£π‘”π‘”π‘ π‘  +π‘£π‘£π‘œπ‘œπ‘œπ‘œπ‘‘π‘‘π‘…π‘…π·π· βˆ₯ π‘Ÿπ‘Ÿπ‘œπ‘œ

=𝑣𝑣𝑖𝑖𝑖𝑖 βˆ’ π‘£π‘£π‘œπ‘œπ‘œπ‘œπ‘‘π‘‘

𝑅𝑅𝐺𝐺

οΏ½1

RSβˆ’ π‘”π‘”π‘šπ‘šοΏ½ 𝑣𝑣𝑖𝑖𝑖𝑖 = οΏ½

1𝑅𝑅𝐺𝐺

+1

𝑅𝑅𝐷𝐷 βˆ₯ π‘Ÿπ‘Ÿπ‘œπ‘œοΏ½ vout

𝐀𝐀𝐕𝐕 =π’—π’—π’π’π’π’π’π’π’—π’—π’Šπ’Šπ’Šπ’Š

=𝟏𝟏 βˆ’ π’ˆπ’ˆπ’Žπ’Žπ‘Ήπ‘Ήπ‘Ίπ‘Ί

𝟏𝟏 + 𝑹𝑹𝑺𝑺/(𝑹𝑹𝑫𝑫 βˆ₯ 𝒓𝒓𝒐𝒐)

Page 3: [HW1 Solution] 1. V =1.8 V DD - Semiconductor System Labssl.kaist.ac.kr/class/17spring/ee403/hw/HW1_sol.pdfΒ Β· Β Β· 2017-03-23[HW1 Solution] 1. 1. Rin= 𝑅𝑅1βˆ₯𝑅𝑅2β‰₯20π‘˜π‘˜Ξ©

4.

(a)

with ID = 0.5mA, VG = 2𝑉𝑉,𝑉𝑉𝐺𝐺 = 1𝑉𝑉.𝑉𝑉𝐺𝐺𝐺𝐺 = 1𝑉𝑉.𝑉𝑉𝑂𝑂𝑂𝑂 = 0.3𝑉𝑉

0.5mA =12

π‘˜π‘˜π‘–π‘–π‘‰π‘‰π‘‚π‘‚π‘‚π‘‚2 ,πŸ•πŸ•π’π’ = 𝟏𝟏𝟏𝟏.πŸπŸπ’Žπ’ŽπŸπŸ/π‘½π‘½πŸπŸ

𝐕𝐕𝐃𝐃 = πŸ“πŸ“ βˆ’ (πŸ“πŸ“πŸ’πŸ’)(𝟎𝟎.πŸ“πŸ“π’Žπ’ŽπŸπŸ) = 𝟐𝟐.πŸ“πŸ“π‘½π‘½

𝐕𝐕𝐆𝐆𝐃𝐃 = βˆ’πŸŽπŸŽ.πŸ“πŸ“π‘½π‘½ < 𝑽𝑽𝒐𝒐 ∢ π‘΄π‘΄πŸ‘πŸ‘ π’Šπ’Šπ’Šπ’Š π’Šπ’Šπ’Šπ’Š π‘Ίπ‘Ίπ‘Ίπ‘Ίπ’π’π’π’π’“π’“π‘Ίπ‘Ίπ’π’π’Šπ’Šπ’π’π’Šπ’Š π‘Ήπ‘Ήπ‘Ήπ‘Ήπ’ˆπ’ˆπ’Šπ’Šπ’π’π’Šπ’Š

(b)

𝐑𝐑𝐒𝐒𝐒𝐒 = πŸπŸπŸŽπŸŽπŸŽπŸŽπŸ’πŸ’ βˆ₯ πŸ‘πŸ‘πŸŽπŸŽπŸŽπŸŽπŸ’πŸ’ = πŸπŸπŸπŸπŸŽπŸŽπŸ’πŸ’π›€π›€

AV =π‘£π‘£π‘œπ‘œπ‘£π‘£π‘ π‘ π‘–π‘–π‘”π‘”

= βˆ’π‘…π‘…π‘–π‘–π‘–π‘–

120π‘˜π‘˜ + π‘…π‘…π‘–π‘–π‘–π‘–π‘”π‘”π‘šπ‘š(5π‘˜π‘˜ βˆ₯ π‘Ÿπ‘Ÿπ‘œπ‘œ βˆ₯ 5π‘˜π‘˜)

gm =2𝐼𝐼𝐷𝐷𝑉𝑉𝑂𝑂𝑂𝑂

= 3.33π‘šπ‘šπ‘šπ‘š, π‘Ÿπ‘Ÿπ‘œπ‘œ =𝑉𝑉𝐴𝐴𝐼𝐼𝐷𝐷

= 100π‘˜π‘˜Ξ©

𝐀𝐀𝐕𝐕 = βˆ’πŸ’πŸ’.𝟎𝟎𝟎𝟎

(c)

𝑉𝑉sig = 𝑉𝑉𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 sin𝑀𝑀𝑀𝑀 ,π‘‰π‘‰π‘œπ‘œ = π‘‰π‘‰π‘œπ‘œ,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 sin𝑀𝑀𝑀𝑀

gm(5π‘˜π‘˜ βˆ₯ 5π‘˜π‘˜ βˆ₯ 100π‘˜π‘˜) = 8.12

Vgd + 𝑉𝑉𝐺𝐺𝐷𝐷 = π‘£π‘£π‘œπ‘œ,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 +π‘£π‘£π‘œπ‘œ,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

8.12βˆ’ 0.5 ≀ 𝑉𝑉𝑑𝑑 = 0.7 𝑉𝑉

𝐕𝐕𝒐𝒐,π’‘π’‘π‘Ήπ‘Ήπ‘Ίπ‘ΊπŸ’πŸ’ < 𝟏𝟏.πŸŽπŸŽπŸ•πŸ•π‘½π‘½

5V

300kΞ© 5kΞ©

5kΞ©

2kΞ©

Vo

M3Vsig

Rin

200kΞ©

120kΞ© CC1

CS

CC2

Page 4: [HW1 Solution] 1. V =1.8 V DD - Semiconductor System Labssl.kaist.ac.kr/class/17spring/ee403/hw/HW1_sol.pdfΒ Β· Β Β· 2017-03-23[HW1 Solution] 1. 1. Rin= 𝑅𝑅1βˆ₯𝑅𝑅2β‰₯20π‘˜π‘˜Ξ©

π•π•π’‘π’‘π‘Ήπ‘Ήπ‘Ίπ‘ΊπŸ’πŸ’ <𝑽𝑽𝒐𝒐,π’‘π’‘π‘Ήπ‘Ήπ‘Ίπ‘ΊπŸ’πŸ’

πŸπŸπ‘½π‘½= πŸπŸπŸŽπŸŽπŸπŸπŸπŸπ•π•

(d)

Vgs = 𝑂𝑂𝑔𝑔1+π‘”π‘”π‘šπ‘šπ‘…π‘…π‘†π‘†

= 𝑣𝑣𝑔𝑔2 when 𝐑𝐑𝐒𝐒 = 𝟏𝟏

π’ˆπ’ˆπ’Žπ’Ž= πŸ‘πŸ‘πŸŽπŸŽπŸŽπŸŽπ›€π›€

(Also correct if you’ve considered 2kΞ© resistor.

The above solution ignored 2kΞ© resistor considering 2kΞ©||300Ξ© β‰’ 300Ξ©)

gm𝑅𝑅𝐿𝐿′1 + π‘”π‘”π‘šπ‘šπ‘…π‘…πΊπΊ

= οΏ½π‘‰π‘‰π‘œπ‘œπ‘‰π‘‰π‘”π‘”οΏ½ = 4.06

Vo,peak +π‘‰π‘‰π‘œπ‘œ,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

4.06βˆ’ 0.5V ≀ 0.7V

𝐕𝐕𝐨𝐨,π©π©π©π©π©π©πŸ•πŸ• = 𝟎𝟎.πŸ—πŸ—πŸŽπŸŽπ‘½π‘½

5.

(a)

ID = 0.3π‘šπ‘šπ‘šπ‘š, |𝑉𝑉𝑂𝑂𝑂𝑂| = 0.3𝑉𝑉

VSG = 1.0𝑉𝑉,𝑉𝑉𝐺𝐺 = 0𝑉𝑉,𝑉𝑉𝐺𝐺 = 2.5 βˆ’ 𝐼𝐼𝐷𝐷𝑅𝑅𝐺𝐺 = 1.0𝑉𝑉

𝐑𝐑𝐒𝐒 = πŸ“πŸ“.πŸŽπŸŽπŸ’πŸ’π›€π›€

(b)

2.5V

RS

VoM3Vsig

Rsig

CC

-2.5V

RD

CS

Page 5: [HW1 Solution] 1. V =1.8 V DD - Semiconductor System Labssl.kaist.ac.kr/class/17spring/ee403/hw/HW1_sol.pdfΒ Β· Β Β· 2017-03-23[HW1 Solution] 1. 1. Rin= 𝑅𝑅1βˆ₯𝑅𝑅2β‰₯20π‘˜π‘˜Ξ©

gm =2𝐼𝐼𝐷𝐷𝑉𝑉𝑂𝑂𝑂𝑂

= 2π‘šπ‘šπ‘šπ‘š,π‘šπ‘šπ‘‚π‘‚ =π‘£π‘£π‘œπ‘œπ‘£π‘£π‘ π‘ π‘–π‘–π‘”π‘”

= βˆ’π‘”π‘”π‘šπ‘šπ‘…π‘…π·π· = βˆ’10

𝐑𝐑𝐃𝐃 = πŸ“πŸ“.πŸŽπŸŽπŸ’πŸ’π›€π›€

(c)

Vgd + 𝑉𝑉𝐺𝐺𝐷𝐷 β‰₯ 𝑉𝑉𝑑𝑑𝑝𝑝 = βˆ’0.7

βˆ’ οΏ½π‘£π‘£π‘œπ‘œ,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 +π‘£π‘£π‘œπ‘œ,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

10οΏ½+ 1𝑉𝑉 β‰₯ βˆ’0.7𝑉𝑉

𝐯𝐯𝐨𝐨,π©π©π©π©π©π©πŸ•πŸ• ≀ 𝟏𝟏.πŸ“πŸ“πŸ“πŸ“π‘½π‘½

π―π―π©π©π©π©π©π©πŸ•πŸ• ≀𝒗𝒗𝒐𝒐,π’‘π’‘π‘Ήπ‘Ήπ‘Ίπ‘ΊπŸ’πŸ’

𝟏𝟏𝟎𝟎= 𝟎𝟎.πŸπŸπŸ“πŸ“πŸ“πŸ“π‘½π‘½

(d)

vpeak = 50π‘šπ‘šπ‘‰π‘‰, change RD

βˆ’ οΏ½π‘£π‘£π‘œπ‘œ,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝 +π‘£π‘£π‘œπ‘œ,𝑝𝑝𝑝𝑝𝑝𝑝𝑝𝑝

π‘”π‘”π‘šπ‘šπ‘…π‘…π·π·οΏ½ + (2.5 βˆ’ 𝐼𝐼𝐷𝐷𝑅𝑅𝐷𝐷) β‰₯ βˆ’0.7𝑉𝑉

for gm = 2 π‘šπ‘šπ‘šπ‘š, 𝐼𝐼𝐷𝐷 = 0.3π‘šπ‘šπ‘šπ‘š

βˆ’ οΏ½1 + π‘”π‘”π‘šπ‘šπ‘…π‘…π·π·π‘”π‘”π‘šπ‘šπ‘…π‘…π·π·

οΏ½ π‘”π‘”π‘šπ‘šπ‘…π‘…π·π·π‘£π‘£π‘π‘π‘π‘π‘π‘π‘π‘ + 2.5 βˆ’ 𝐼𝐼𝐷𝐷𝑅𝑅𝐷𝐷 β‰₯ βˆ’0.7

𝐑𝐑𝐃𝐃 ≀ πŸ•πŸ•.πŸ–πŸ–πŸ–πŸ–πŸ’πŸ’π›€π›€, 𝐀𝐀𝐕𝐕 = βˆ’π’ˆπ’ˆπ’Žπ’Žπ‘Ήπ‘Ήπ‘«π‘« = βˆ’πŸπŸπŸ“πŸ“.πŸ–πŸ–


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