ECE 3050 Analog Electronics - BJT Formula Summary · PDF fileECE 3050 Analog Electronics - BJT...
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ECE 3050 Analog Electronics - BJT Formula Summary Equations are for the npn BJT. For the pnp device, reverse the directions of all current labels and reverse the order of subscripts involving node labels, i.e. V CE becomes V EC . When more than one equation is given, either can be used. i C = I S e v BE /V T I S = I S0 μ 1+ v CE V A ¶ i B = i C β i E = i C + i B β = β 0 μ 1+ v CE V A ¶ g m = I C V T r π = V T I B = (1 + β) r e r e = V T I E = r π 1+ β = α g m r 0 = V A + V CE I C α = β 1+ β β = α 1 − α r e α = r π β r 0 e = R tb + r x + r π 1+ β = R tb + r x 1+ β + r e i 0 c = g m v b 0 e = αi 0 e = βi b i c(sc) = G mb v tb − G me v te G mb = α r 0 e + R te kr 0 r 0 − R te /β r 0 + R te G me = 1 R te + r 0 e kr 0 αr 0 + r 0 e r 0 + r 0 e r ic = r 0 + r 0 e kR te 1 − αR te / (r 0 e + R te ) R tb =0,rx=0 = r 0 [1 + g m (r π kR te )] + R te v e(oc) = v tb r 0 + R tc / (1 + β ) r 0 e + r 0 + R tc / (1 + β ) r ie = r 0 e r 0 + R tc r 0 e + r 0 + R tc / (1 + β ) v b(oc) = v te r 0 + R tc R te + r 0 + R tc r ib = r x + (1 + β ) r e + R te (1 + β ) r 0 + R tc r 0 + R te + R tc = r x + r π + R te (1 + β) r 0 + R tc r 0 + R te + R tc r 0 large = r x + r π + (1 + β) R te r 0 Approximations — Assume r 0 = ∞ except when calculating r ic i 0 e = i e i c(sc) = i 0 c = αi e = βi b = G m (v tb − v te ) G m = α r 0 e + R te r 0 e = R tb + r x + r π 1+ β = R tb + r x 1+ β + r e r ic = r 0 + r 0 e kR te 1 − αR te / (r 0 e + R te ) v e(oc) = v tb r ie = r 0 e v b(oc) = v te r ib = r x + r π + (1 + β) R te = r x + (1 + β )(r e + R te ) 1
Transcript of ECE 3050 Analog Electronics - BJT Formula Summary · PDF fileECE 3050 Analog Electronics - BJT...
ECE 3050 Analog Electronics - BJT Formula Summary
Equations are for the npn BJT. For the pnp device, reverse the directions of all current labels and reversethe order of subscripts involving node labels, i.e. VCE becomes VEC . When more than one equation isgiven, either can be used.
iC = ISevBE/VT IS = IS0
µ1 +
vCEVA
¶iB =
iCβ
iE = iC + iB β = β0
µ1 +
vCEVA
¶gm =
ICVT
rπ =VTIB
= (1 + β) re re =VTIE
=rπ1 + β
=α
gmr0 =
VA + VCEIC
α =β
1 + β
β =α
1− α
reα=
rπβ
r0e =Rtb + rx + rπ
1 + β=
Rtb + rx1 + β
+ re i0c = gmvb0e = αi0e = βib
ic(sc) = Gmbvtb −Gmevte Gmb =α
r0e +Rtekr0r0 −Rte/β
r0 +RteGme =
1
Rte + r0ekr0αr0 + r0er0 + r0e
ric =r0 + r0ekRte
1− αRte/ (r0e +Rte)
Rtb=0, rx=0= r0 [1 + gm (rπkRte)] +Rte ve(oc) = vtbr0 +Rtc/ (1 + β)
r0e + r0 +Rtc/ (1 + β)
rie = r0er0 +Rtc
r0e + r0 +Rtc/ (1 + β)vb(oc) = vte
r0 +Rtc
Rte + r0 +Rtc
rib = rx + (1 + β) re +Rte(1 + β) r0 +Rtc
r0 +Rte +Rtc= rx + rπ +Rte
(1 + β) r0 +Rtc
r0 +Rte +Rtc
r0 large= rx + rπ + (1 + β)Rte
r0 Approximations — Assume r0 =∞ except when calculating ric
i0e = ie ic(sc) = i0c = αie = βib = Gm (vtb − vte) Gm =α
r0e +Rte
r0e =Rtb + rx + rπ
1 + β=
Rtb + rx1 + β
+ re ric =r0 + r0ekRte
1− αRte/ (r0e +Rte)ve(oc) = vtb
rie = r0e vb(oc) = vte rib = rx + rπ + (1 + β)Rte = rx + (1 + β) (re +Rte)
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