ESE319 Introduction to Microelectronics High Frequency BJT Model & Cascode BJT Amplifier Kenneth R. Laker, update 01Oct14 KRL 1 ESE319 Introduction to Microelectronics Gain of 10 Amplifier – Non-ideal Transistor RC R1 C in V CC RS R2 RE v s Gain starts dropping at > 1MHz. Why! Because of internal transistor capacitances that we have ignored in our low frequency and mid-band models. Kenneth R. Laker, update 01Oct14 KRL 2 ESE319 Introduction to Microelectronics Sketch of Typical Voltage Gain Response for a CE Amplifier ∣Av∣dB Low Midband High Frequency ALL capacitances are neglected, i.e. Frequency Band External C's s.c. Band Internal C's o.c. Due to external blocking and by- 3dB Due to BJT parasitic pass capacitors. capacitors Cπ and Cµ. External C's s.c. Internal C's o.c. 20log10∣Av∣dB f Hz f L f H (log scale) BW = f H − f L≈ f H GBP=∣Av−mid∣BW Kenneth R. Laker, update 01Oct14 KRL 3 ESE319 Introduction to Microelectronics High Frequency Small-signal Model (Fwd. Act.) C r x C v be Two capacitors and a resistor added to mid-band small signal model. ● base-emitter capacitor, Cµ ● base-collector capacitor, Cπ ● resistor, , representing the base terminal resistance ( ); rx rx << rπ ignored in hand calculations. Kenneth R. Laker, update 01Oct14 KRL 4 ESE319 Introduction to Microelectronics High Frequency Small-signal Model (Fwd. Act.) SPICE/MultiSim C r x CJC = C µ0 CJE = C je0 TF = τ C F RB = r v x be C =C deC je≈C de2C je0≈C de C 0 C je0 C = C = I C m je m C g i V CB V EB de= m F= F Note C= dt 1 1 V T d v 0cb 0eb C ≈2C 0 C = base-charging (diffusion) cap Non-linear, voltage controlled de = forward-base transit time m = junction grading coefficient 0.2 to 0.5) τF Kenneth R. Laker, update 01Oct14 KRL 5 ESE319 Introduction to Microelectronics High Frequency Small-signal Model (IC) C π C µ C = collector-substrate depletion capacitance, ignored in hand calcs. CS Kenneth R. Laker, update 01Oct14 KRL 6 ESE319 Introduction to Microelectronics High Frequency Small-signal Model The transistor parasitic capacitances have a strong effect on circuit high frequency performance! ● C attenuates base signal, decreasing v since X → 0 (short circuit) π be Cπ at very high-frequencies. ● ● As we will see later; is principal cause of gain loss at high-frequencies. Cµ At the base base-collector looks like a capacitor of value between Cµ k Cµ base-emitter, where k > 1 and may be >> 1. C r x C ● This phenomenon is called the Miller Effect. Kenneth R. Laker, update 01Oct14 KRL 7 ESE319 Introduction to Microelectronics Prototype Common Emitter Circuit V CC C R C RS b c vo RS C in vo + v R r be g v B vs RB C m be R vs - C R C V B E byp e At high frequencies High frequency large blocking and bypass small-signal ac model capacitors are “short circuits” Kenneth R. Laker, update 01Oct14 KRL 8 ESE319 Introduction to Microelectronics Multisim Simulation C 2 pF RS 50 b c vo v v RB r be g v Mid-band gain @ 100 kHz s C m be RC 50k 40mS v 2.5k 12 pF be 5.1k e o Av−mid=−g m RC=−20446dB@ 180 Gain @ 8.69 MHz Kenneth R. Laker, update 01Oct14 KRL 9 ESE319 Introduction to Microelectronics Introducing the Miller Effect C RS b c vo v v RB r be g m vbe s C RC e The feedback connection of C between base-collector causes it to appear in the amplifier like a large capacitor 1 − K C between the base-emitter terminals. This phenomenon is called the “Miller effect” and capacitor multiplier “1 – K ” acting on C equals the CE amplifier mid-band gain, i.e. K=Av−mid =−g m RC NOTE: CB and CC amplifiers do not suffer from the Miller effect, since in these amplifiers, one side of C is connected directly to ground. Kenneth R. Laker, update 01Oct14 KRL 10 ESE319 Introduction to Microelectronics Miller's Theorem 1 Z= j 2 f C C R S b c v I Z −I o + + i -i r vbe g v V vs RB C m be R be V o C <=> Av−mid V be - - e RB∥r ≫RS V o =Av−mid=−g m RC V be vo vo Av−mid= ≈ =−g m RC vs vbe Kenneth R. Laker, update 01Oct14 KRL 11 ESE319 Introduction to Microelectronics Miller's Theorem I I I 2=−I = 1 Z I 1=I I 2=−I + + + + V 1 Av V 1 V 2 V 1 Z Z V 2=Av V 1 <=> 1 2 - - - - V 1 V 1 Z V 1−V 2 V 1− Av V 1 V 1 Z 1= = = I =I 1= = = => Z Z Z I 1 I 1−Av 1−Av 1 Z 1= 1 j 2 f C 1−Av V 2− V 2 V 2−V 1 Av V 2 V V Z −I =I = = = 2 2 2 Z 2= = = ≈Z if A >> 1 Z Z Z => I −I 1 v 2 1− 1 A 1− v Ignored in A V V v 2 2 1 practical Z 2= = ≈ I 2 −I j 2 f C circuits Kenneth R. Laker, update 01Oct14 KRL 12 ESE319 Introduction to Microelectronics Common Emitter Miller Effect Analysis Determine effect of C : I C C Using phasor notation: RS V be I =−g V I b c RC m be C V o I or RC V be V RB r g m V be V o=I R RC = −g m V beI C RC s C RC C where e 1 I V V C = be− o j 2 f C I C = V beg m V be RC−I C RC j 2 f C Note: The current through C depends only on V be ! 1g m RC j2 f C I C = V be 1 j2 f R C C Kenneth R. Laker, update 01Oct14 KRL 13 ESE319 Introduction to Microelectronics Common Emitter Miller Effect Analysis II I C C V RS b be c From slide 13: V o I R 1g R j2 f C C m C vbe V R r g m V be I C = V be s B C RC 1 j2 f R C C e 1g m RC j2 f C I C = V be≈ 1g m RC j2 f C V be= j2 f C eq V be 1 j2 f R C C 2 f RC C ≪1 Miller Capacitance C : C =1g R C =1−A C eq eq m C v Kenneth R. Laker, update 01Oct14 KRL 14 ESE319 Introduction to Microelectronics I I C C C C V R V RS be S b be c b c V o V o I RC I R g V C V s RB r m be r g V C RC V s RB C m be R C C C eq e e C eq=1−AvC =1g m RC C Kenneth R. Laker, update 01Oct14 KRL 15 ESE319 Introduction to Microelectronics Common Emitter Miller Effect Analysis III C eq=1g m RC C For our example circuit (C = 2 pF): µ 1g m RC=10.040⋅5100=205 C eq=205⋅2 pF≈410 pF Kenneth R. Laker, update 01Oct14 KRL 16 ESE319 Introduction to Microelectronics Simplified HF Model C RS V be I b C c V o vbe g V ' V s RB r C m be R r R R ro RC RL L= o∥ C∥ L e C ' RB∥r ' RS V be I V s=V s b C c V o RB∥rRS ' ' v RS =r∥ RB∥RS r be g V ' V s RB C m be RL e Thevenin Equiv. Kenneth R. Laker, update 01Oct14 KRL 17 ESE319 Introduction to Microelectronics Simplified HF Model C ' R' r R R RS I L= o∥ C∥ L b C c V o ' R =r ∥ R ∥R V be S B S ' RB∥r ' r g V ' V s RB C m be V s=V s RL RB∥rRS e Miller's Theorem ' RS b c V o I V be C ' r g V ' V s RB m be C C eq RL C eq=1g m RC C e C C C tot = eq C tot Kenneth R. Laker, update 01Oct14 KRL 18 ESE319 Introduction to Microelectronics Simplified HF Model R' S b c V V o ' I be RL=ro∥RC∥RL C ' r g V ' ' V s RB m be C C eq RL RS =r∥ RB∥RS ' RB∥r e V s=V s ≈V s RB∥r RS C tot C tot =C 1g m RC C V o 1 j2 f C dB / tot V V be= V s ' ∣ s∣ 1/ j2 f C totRS ' ' ' V o −g m RL −g m RL Av f = ≈ ' = V s 1 j 2 f C R f tot S 1 j f H ' 1 Av−mid=−g m RL and f H = ' 2C tot RS Kenneth R. Laker, update 01Oct14 KRL 19 ESE319 Introduction to Microelectronics Multisim Simulation C 2 pF RS 50 b c vo v v RB r be g v s C m be RC 50k 40mS v 2.5k 12 pF be 5.1k Mid-band gain @ 100 kHz e o Av−mid=−g m RC=−20446dB@ 180 C tot=12 pF205⋅2 pF ≈422 pF 1 1 f H ≈ f −3dB= ' ≈ ≈7.54 MHz Gain @ 8.69 MHz 2C tot RS 2 422 pF 50 Kenneth R.