Microelectronic Circuits II Ch8 :...
Transcript of Microelectronic Circuits II Ch8 :...
![Page 1: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/1.jpg)
CNU EE 8.1-1
Microelectronic Circuits II
Ch 8 : Frequency Response
8.1 Low-Frequency Response of CS & CE Amplifier
![Page 2: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/2.jpg)
CNU EE 8.1-2
Introduction- gain is constant independent of the frequency of the input signal à infinite bandwidth à Not true,- midband : gain remains almost constant over a wide frequency range
coupling & bypass capacitors à short, internal capacitance à open- lower freq. band : coupling & bypass capacitors no longer have low impedance,
fL : lower end of mid-frequency, reactance 1/jwC- high freq. band : internal capacitance of transistor no longer have high impedance,
fH : upper end of mid-frequency , reactance 1/jwC- Amplifier bandwidth = fH – fL- Extension of bandwidth (i.e., increase fH) à source degeneration resistances
Magnitude of the gain of a discrete BJT or MOS amplifier vs. frequency
![Page 3: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/3.jpg)
CNU EE 8.1-3
Appendix E : STC (Single Time Constant) circuits
- single-time-constant (STC) circuits : one reactive component (L or C) & one resistance R- An STC circuit : time constant t = L/R or CR- Evaluating the time constant
1) reduce the excitation to zero : voltage source à short, current source à open2) find equivalent resistance Req seen by the one reactive component : Req=R4||[R3+(R2||R1)]3) time constant is either L/Req or CReq t =C{R4||[R3+(R2||R1)]}
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CNU EE 8.1-4
Classification of STC circuits- Two categories : low-pass (LP) & high-pass (HP) types- low-pass circuits pass dc (i.e., signals w/ zero freq.) and attenuate high freq. w/ zero transmission at w=- At w = 0 , capacitor à open circuit (1/jwC = ), inductor à short circuit (jwL = 0 )- At w = , capacitor à short circuit (1/jwC = 0 ), inductor à open circuit (jwL = )
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low-pass type high-pass type
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CNU EE 8.1-5
Low-Pass circuits- STC low-pass circuit transfer function
K: gain at w=0, w0=1/t t :time constant- Magnitude response, phase response
- Magnitude axis (dB) : 20log|T(jw)/K|- freq. axis (rad/sec):logarithmic scale(w/w0)- low-frequency asymptote |T(jw)| ~ 1~0dB- w/w0 >> 1 : if w doubles, |T(jw)| is halvedà slope : -6dB/octave, -20dB/decade
- two straight-line asymptotes of the magnitude – response curve meet at the Corner freq. or break freq. w0
- w =w0 , gain drops by a factor of relative to the dc gain à corner freq. = 3-dB frequency
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![Page 6: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/6.jpg)
CNU EE 8.1-6
High-Pass circuits- STC high-pass circuit transfer function
K: gain at w= , w0=1/t t :time constant- Magnitude response, phase response
- Magnitude axis (dB) : 20log|T(jw)/K|- freq. axis (rad/sec):logarithmic scale(w/w0)- high-frequency asymptote |T(jw)| ~ 1~0dB- w/w0 << 1: if w doubles, |T(jw)| is doubledà slope : +6dB/octave, +20dB/decade
- two straight-line asymptotes of the magnitude – response curve meet at the Corner freq. or break freq. w0
- w =w0 , gain drops by a factor of relative to the gain at high frequencyà corner freq. = 3-dB frequency
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CNU EE 8.1-7
Frequency response of STC networks
![Page 8: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/8.jpg)
CNU EE 8.1-8
MOSFET 등가회로
§ Small-signal equivalent circuit models
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§ saturation mode
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![Page 9: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/9.jpg)
CNU EE 8.1-9
§ frequency independent analysis- CC1, CC2,: coupling capacitor- CS (mF): bypass capacitor- Effect of capacitances on gain Vo/Vsig- at midband frequencies, CC1, CC2,CS (mF)ànegligibly small impedances, and
assume perfect short circuità midband gain
- at low frequencies, reactance 1/jwC of CC1, CC2,CS (mF) increases & amplifier gain decreases
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Low-Frequency response of CS amplifier
§ three frequency bands- midband : useful band of amplifier- low-frequency band : CC1, CC2,CS- high-frequency band : Cgs, Cgd
![Page 10: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/10.jpg)
CNU EE 8.1-10
Low-frequency response of CS amplifier§ Determining Vo/Vsig at low frequency- current source I : open- voltage source VDD : short- direct small-signal analysis (No ro)- Determining Vg, Id, Io, & Vo
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Coupling capacitor CC1 introduces a high-pass STC response w/ a break frequency
§ Drain current Id from amplifier input Vg
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gd C
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wCS introduces a frequency-dependent factor& STC high-pass type w/ a break frequency wP2
T model
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CNU EE 8.1-11
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Low-frequency response of CS amplifier
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CC2 introduces a 3rd high-pass factorw/ a 3rd break frequency at
§ Overall low-frequency transfer function of CS amplifier3
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AM : Midband gain with CC1, CC2,CS acting as perfect short circuits
![Page 12: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/12.jpg)
CNU EE 8.1-12
Low-frequency response of CS amplifier§ Determining lower 3-dB frequency, fL- Lower 3-dB frequency, fL = frequency at
which |Vo/Vsig| drops to |AM|/- If the break frequency wP1, wP2, & wP3
are sufficiently separated, their effectappear distinct.
- At each break frequency, gain slope increases by 20dB/decade
- fP1, fP2 & fP3 : low-frequency poles- If the highest-frequency pole, fP2, is
separated from the nearest pole, fP3 by atleast a factor of 4 (two octaves) :
- The highest pole, fP2 ~ Cs because Csinteracts with 1/gm, which is low
§ Determining the pole frequencies by inspection1. Reduce Vsig to zero2. Consider each capacitor separately; that is, assume that the other two capacitors are acting as
perfect short circuits3. For each capacitor, find the total resistance seen between its terminals. This is the resistance that
determines the time constant associated with this capacitor
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CNU EE 8.1-13
BJT 등가회로§ Small-signal equivalent circuit models
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![Page 14: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/14.jpg)
CNU EE 8.1-14
Low-frequency response of CE amplifier§ frequency independent analysis
- CC1, CC2,CE (mF): short circuit- Cp , Cm (pF range): open circuit- |AM| = constant in the midband
§ three frequency bands- midband : useful band of amplifier- low-frequency band : CC1, CC2,CE- high-frequency band : Cp , Cm
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§ bandwidth or 3-dB bandwidthBW = fH – fL
~ fH when fL << fH§ gain-bandwidth product
GB = |AM|BW: trade-off gain for bandwidth
![Page 15: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/15.jpg)
CNU EE 8.1-15
Low-frequency response of CE amplifier
§ Simple circuit for Low Frequency response- current source I : open- voltage source VCC : short- ignore Cp & Cm : open- neglect rx since rx << rp§ Analysis of the low-frequency response of the CE amplifier
- consider the effect of the three capacitors CC1, CE & CC2 one at a time
T model
![Page 16: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/16.jpg)
CNU EE 8.1-16
Low-frequency response of CE amplifier
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§ Effect of CC1 with CE & CC2 short-circuited
§ [(RB||rp+Rsig] is the resistance seen between the terminals of CC1 when vsig = 0
CC1 introduces a STC high-passtype w/ a break frequency wP1
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![Page 17: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/17.jpg)
CNU EE 8.1-17
Low-frequency response of CE amplifier
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§ Effect of CCE with CC1 & CC2 short-circuited & utilizing Thevenin theorem
§ [re+((RB||Rsig)/(b+1))] is the resistance seen between the two terminals of CE when vsig = 0
CE introduces a STChigh-pass type w/ a break frequency wP2
T 모델
![Page 18: Microelectronic Circuits II Ch8 : FrequencyResponsecontents.kocw.net/KOCW/document/2014/Chungnam/chahanju/06.pdf · 8.1 Low-Frequency Response of CS & CE Amplifier. CNU EE 8.1-2 Introduction-gainis](https://reader033.fdocuments.net/reader033/viewer/2022051812/602adea43c7bb02f3b487a69/html5/thumbnails/18.jpg)
CNU EE 8.1-18
Low-frequency response of CE amplifier
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§ Effect of CC2 with CE & CC1 short-circuited
§ (RC+RL) is the resistance seen between the terminals of CC2 when vsig = 0
CC2 introduces a STC high-passtype w/ a break frequency wP3
p 모델
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CNU EE 8.1-19
Low-frequency response of CE amplifier
§ Overall low-frequency transfer function of CE amplifier
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§ 3-dB frequency fL is determined by the highest of the three break frequencies the break frequency is caused by the bypass capacitor CE , that is fL ~ fP2