figs08 2nd edition - Academics |...
42
R. Ludwig and G. Bogdanov “RF Circuit Design: Theory and Applications” 2 nd edition Figures for Chapter 8 Figure 8-1 Eight possible configurations of discrete two-component matching networks. L L C C (a) (b) (c) (d) Z S Z L Z S Z L Z S Z L Z S Z L C 1 C 2 L C C (e) (f) (g) (h) L 2 L 1 Z S Z L Z L Z S L 2 L 1 Z S L Z L Z L C 2 C 1 Z S
Transcript of figs08 2nd edition - Academics |...
R. Ludwig and G. Bogdanov“RF Circuit Design: Theory and Applications”
2nd edition
Figures for Chapter 8
Figure 8-1 Eight possible configurations of discrete two-component matching networks.
L L
C C
(a) (b) (c) (d)
ZS ZL ZS ZL ZS ZL ZS ZL
C1C2
L
C C
(e) (f) (g) (h)
L2
L1ZS ZL ZLZS L2
L1
ZS
L
ZL ZL
C2C1
ZS
Figure 8-2 Transmitter to antenna matching circuit design.
L
CTransmitter
ZM
ZAZT
Figure 8-3 Impedance effect of series and shunt connections of L and C to a complex load in the Smith Chart.
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Shunt L
Series C
Series L
Shunt C
Figure 8-4 Design of the two-element matching network as part of the ZY Smith Chart.
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L
CC
ZT
ZT
ZT
zTC = 12j1.22
zT = 21j1
zM = zA* = 12j0.2
Figure 8-5 Design of a matching network using the Smith Chart
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zL*
A D
B C
zS
Figure 8-6 Matching networks for four different paths in the Smith Chart.
→ →zS zA zL*
L1 = 1.59 nH
L2 = 6.63 nHZS ZL 2.23 pF
6.37 nH
ZS ZL
→ →zS zB zL*
0.94 pF
3.06 nH
→ →zS zC zL*
ZS ZL
2.79 nH
13.26 nHZS ZL
→ →zS zD zL*
Fig
ure
8-7
For
bidd
en r
egio
ns fo
r L-
type
mat
chin
g ne
twor
ks w
ith Z
S =
Z0
= 5
0 Ω
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(a)
(c)
(b)
(d)
ZS
ZL
ZS
ZL
ZS
ZL
ZS
ZL
Figure 8-8 Two design realizations of an L-type matching network.
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zS
A
B
zL
(b)
RS = 50 Ω C = 2.6 pF CL Vout
L = 10 nH
VS
RL
(c)
VS
RS = 50 Ω L = 9.75 nH
C = 0.6 pF
CLVout
RL
(a) Impedance transformations displayed in Smith Chart
Figure 8-9 Frequency response of the two matching network realizations.
Frequency f, GHz
Circuit in
Figure 8-8(b)
Circuit in
Figure 8-8(c)
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(a) Frequency response of input reflection coefficient
Inp
ut
refl
ecti
on
co
effi
cien
t |Γ
in|
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(b) Transfer function of the matching networks
Circuit in
Figure 8-8(b)
Circuit in
Figure 8-8(c)
Tra
nsf
er f
un
ctio
n H
, d
B
Frequency f, GHz
Figure 8-10 Comparison of the frequency response of the L-type matching network and an equivalent bandpass filter.
(a) Equivalent bandpass filter
RST = 125.1 Ω
Vb
VTCT
1.55 pF
LLN
16.2 nHRLP = 125.1 Ω
Frequency f, GHz
Equivalentfilter
Circuit inFigure 8-8(c)
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(b) Frequency response of the matching network compared to the equivalent
filter response
Tra
nsf
er f
un
ctio
n H
, d
B
Figure 8-11 Constant Qn contours displayed in the Smith Chart.
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Qn = 10
Qn = 3
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Qn = 0.3
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Qn = 1
Qn = 3
Qn = 10
Figure 8-12 Two L-type matching networks for a 50 source and a load impedance operated at a frequency of 1 GHz.
(a) Impedance transformation in the Smith Chart
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A Qn = 1
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Resulting matching networks
(b)
RS = 50 Ω L = 0.8 nH
VS
C = 3.18 pF RL
LL = 3.18 nH Vout
(c)
VS
RS = 50 Ω C = 3.54 pF LL = 3.18 nH
RL
Vout
L = 7.96 nH
Ω ZL 25 j20+( )Ω=
Figure 8-13 Frequency responses for the two matching networks.
3 dB
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Figure 8-12(c)
Figure 8-12(b)
4
Tra
nsf
er f
un
ctio
n H
= V
ou
t/ V
S,
dB
Frequency f, GHz
Figure 8-14 General topology of a T-type matching network.
Z3 Z1
ZL
ZA
Z2
ZBZin
Figure 8-15 Design of a T-type matching network for a specified Qn = 3.
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A
zin
Qn = 3
zL
Figure 8-16 T-type matching network circuit schematics.
L3 = 7.85 nH C1 = 8.72 pF
C2 = 3.53 pF ZL
Zin
Figure 8-17 Design of a Pi-type matching network using a minimal Qn.
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B
A
zin Qn = 2
Qn = 2
zL
Figure 8-18 Pi-type matching network configuration.
C2 = 1.65 pF
ZLL1
1.31 nH
L3
1.66 nH
Zin
Figure 8-19 Mixed design of matching network involving transmission line sections (TL) and discrete capacitive elements.
ZL
TL3 TL2 TL1
C2 C1
Zin
Figure 8-20 Design of the distributed matching network for Example 8-7.
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40-40
50
-50
60
-60
70
-70
80
-80
90
-90
100
-100
110
-110
120
-120
130
-130
140
-140
150
-150
160
-160
170
-170
18
0
0.0
1
0.0
1
0.0
2
0.0
2
0.0
3
0.0
3
0.04
0.04
0.05
0.05
0.06
0.06
0.07
0.07
0.08
0.08
0.09
0.09
0.1
0.1
0.11
0.11
0.12
0.12
0.13
0.13
0.14
0.14
0.15
0.15
0.16
0.16
0.17
0.17
0.18
0.18
0.19
0.19
0.2
0.20.21
0.210.2
2
0.2
20.2
3
0.2
3
0.2
4
0.2
4
0.2
5
0.2
5
0.2
6
0.2
6
0.2
7
0.2
7
0.2
8
0.2
8
0.29
0.29
0.3
0.3
0.31
0.31
0.32
0.32
0.33
0.33
0.34
0.34
0.35
0.35
0.36
0.36
0.37
0.37
0.38
0.38
0.39
0.39
0.4
0.4
0.41
0.41
0.42
0.42
0.43
0.43
0.44
0.44
0.45
0.45
0.46
0.46
0.4
7
0.4
70.4
8
0.4
8
0.4
9
0.4
9
0.0
0.0
zin
A
B
l2 = 0.26
l 1 =
0.055
zL
Figure 8-21 Matching network combining series transmission lines and shunt capacitance.
l2 = 0.26 l1 = 0.055
ZL
Zin
C1 = 4.37 pF
Figure 8-22 Input impedance as a function of the position of the shunt capacitor in Example 8-7.
Distance l,
No
rmal
ized
in
pu
t re
acta
nce
, x i
n
xin
rin
0 0.05 0.1 0.15 0.2 0.25 0.3 0.35
3.5
3
2.5
2
1.5
0.5
1
2
1.5
1
0.5
0
20.5
21
No
rmal
ized
in
pu
t re
sist
ance
, r i
n
l = l1
Figure 8-23 Two topologies of single-stub matching networks.
Open or
short circuitOpen or
short circuit
(a) (b)
Z0L, lL
Zin
Z0S
lSZL
Z0L, lL
ZLZ0S
lSZin
Figure 8-24 Smith Chart design for the single-stub matching network based on Example 8-8.
0.2
0.2
0.2
0.50.5
0.5
1.0
1.0
1.0
2.02.0
2.0
5.0
5.0
5.0
0.5
0.5
0.5
0.5
2.02.0
2.0
2.0
0.2
0.2
0.2
0.5
0.5
0.5
1.0
1.0
1.0
2.0
2.0
2.0
5.0
5.0
5.0
0.5
0.5
0.5
0.5
2.0
2.0
2.0
2.0
0.2
0.2
0.2
0.50.5
0.5
1.0
1.0
1.0
2.02.0
2.0
5.0
5.0
5.0
0.5
0.5
0.5
0.5
2.02.0
2.0
2.0
0010
-10
20
-20
30-30
40-40
50
-50
60
-60
70
-70
80
-80
90
-90
100
-100
110
-110
120
-120
130
-130
140
-140
150
-150
160
-160
170
-170
18
0
0.0
1
0.0
1
0.0
2
0.0
2
0.0
3
0.0
3
0.04
0.04
0.05
0.05
0.06
0.06
0.07
0.07
0.08
0.08
0.09
0.09
0.1
0.1
0.11
0.11
0.12
0.12
0.13
0.13
0.14
0.14
0.15
0.15
0.16
0.16
0.17
0.17
0.18
0.18
0.19
0.19
0.2
0.20.21
0.210.2
2
0.2
20.2
3
0.2
3
0.2
4
0.2
4
0.2
5
0.2
5
0.2
6
0.2
6
0.2
7
0.2
7
0.2
8
0.2
8
0.29
0.29
0.3
0.3
0.31
0.310.32
0.32
0.33
0.33
0.34
0.34
0.35
0.35
0.36
0.36
0.37
0.37
0.38
0.38
0.39
0.39
0.4
0.4
0.41
0.41
0.42
0.42
0.43
0.43
0.44
0.44
0.45
0.45
0.46
0.46
0.4
7
0.4
70.4
8
0.4
8
0.4
9
0.4
9
0.0
0.0
zL
A
B
l SA
= 0
.067
zin
l LA
= 0
.266
Figure 8-25 Balanced stub design for Example 8-9.
0.25
ST2
TL1
ZLZin ST10
.32
4
Z0S = 107.1 Ω Z0L = 86.6 Ω
0.3
24
Figure 8-26 Double-stub matching network arrangement.
Zin = Z0 ZA ZB ZC ZD
l3 l2 l1
ZLlS1lS2
Open or
short circuit
Figure 8-27 Smith Chart analysis of a double-stub matching network shown in Figure 26.
0.2
0.2
0.2
0.50.5
0.5
1.0
1.0
1.0
2.02.0
2.0
5.0
5.0
5.0
0.5
0.5
0.5
0.5
2.02.0
2.0
2.0
0.2
0.2
0.2
0.5
0.5
0.5
1.0
1.0
1.0
2.0
2.0
2.0
5.0
5.05
.0
0.5
0.5
0.5
0.5
2.0
2.0
2.0
2.0
0.2
0.2
0.2
0.50.5
0.5
1.0
1.0
1.0
2.02.0
2.0
5.0
5.0
5.0
0.5
0.5
0.5
0.5
2.02.0
2.0
2.0
g = 2 circle
Forbidden
region
yB circle (g = 1) 3 /8
yC circle
(3 /8 rotated g = 1 circle)
Figure 8-28 Double-stub matching network design for Example 8-10.
0.2
0.2
0.2
0.50.5
0.5
1.0
1.0
1.0
2.02.0
2.0
5.0
5.0
5.0
0.5
0.5
0.5
0.5
2.02.0
2.0
2.0
0.2
0.2
0.2
0.5
0.5
0.5
1.0
1.0
1.0
2.0
2.0
2.0
5.0
5.0
5.0
0.5
0.5
0.5
0.5
2.0
2.0
2.0
2.0
0.2
0.2
0.2
0.50.5
0.5
1.0
1.0
1.0
2.02.0
2.0
5.0
5.0
5.0
0.5
0.5
0.5
0.5
2.02.0
2.0
2.0
yB
yC
yL
yD
yA
Forbidden
region
3 /8
Figure 8-29 Various classes of amplifier operation.
Output waveform
(a) Class A (b) Class B
(c) Class AB (d) Class C
IC
Linear regionIdeal transfer
function
Quiescent
point
V* VBE
Cutoff region
Input waveform
IC
Quiescent
pointVBE
ΘB = 180˚
Quiescent
point
IC
VBE
IC
Quiescent
point
VBE
Figure 8-30 Load and power supply current waveforms as a function of conduction angle.
(a) Load current waveform at the output of the transistor
0 Θ6π
IL
I0
4π
Θ0
(b) Corresponding power supply current waveform
0
Θ0
Θ4π 6π
IS
IQ + I0
IQ
Θ0/2
2π
2π
Figure 8-31 Maximum theoretical efficiency of an ideal amplifier as a function of conduc-tion angle.
Eff
icie
ncy
,
% = 78.5%Class B
Class AB
Class C
0 5050
55
60
65
70
75
80
85
90
95
100
100
150 200 250 300 350
Class A
Conduction angle, Θ0
Θ0 = 180˚
Figure 8-32 Passive biasing networks for an RF BJT in common-emitter configuration.
(a)
RFC
RFoutRFC
VCC
R1
CB
I1IB
IC
CB
RFin
R2
(b)
RFC
RFCIX
CB
VCC
IC
IB
RFout
RFin
R3
CBR1
VX
R2
R4
Figure 8-33 Active biasing network for a common-emitter RF BJT.
RFC
RFin
RFout
RFC
I1
Q2
Q1
IB1IC1
VC1
IB2
VCC
CB
CB
RB1
RB2
RC1
IC2
RC2
Figure 8-34 Active biasing network containing low-frequency transistor and two diodes.
RFC
RFC
RFin
RFout
R1
D1
Q1
Q2
D2
R2
VCC
CB
CB
Figure 8-35 Modification of the active biasing network shown in Figure 33 for common-base RF operation.
RFC
RFC
RFC
RFin
RFout
Q1
Q2
I1
VCC
CB
CB
RC1
RC2
RB2
IC1
IC2
IB1
IB2
VC1
RB1
Figure 8-36 DC and RF equivalent circuits for the active biasing network in Figure 35.
RFC
RFC
RFC
RFC
RFC
RFC
(a) DC equivalent circuit (b) RF equivalent circuit
RFin
RFout
Q2
Q1
Q2
Q1
VCCVCC
CB
CB
CB
CB
RC2
RC1RB1
RB2RB2
RC1 RB1
RC2
Figure 8-37 Bipolar passive biasing network for FETs.
RFC RFC
RFin
RFout
CB
VDVG
CB
Figure 8-38 Unipolar passive biasing networks for FETs.
RFC
RFCRFC
RFC
RFC
RFinRFin
RFoutRFout
RS
VD
CB
CB
VS
CB
VD
CB
Figure 8-39 E-pHEMT biasing network: (a) DC bias circuit, (b) DC model, (c) low-frequency small-signal model.
(b) (c)
(a)
R2R1
R3 R4
X1
Q2Q1
VDDVDD
VD
ID
VG
IR3
R2R1
+ +
– –
R3 R4
X1
VDD VDD
VD
VG
|VBE1| |VBE2|IB2IB1
IB1
ID
IR3
R2R1
R3
re1 re2
R4
id
vg
ib2ib1
iB1 iB2IB2
Figure 8-40 Conceptual PCB layout of the 7 GHz amplifier, showing the biasing filters and matching networks implemented with microstrips.
ATF551M4
/4
L1 L2
S1 S2
ΓMS
ΓML
VDS
RFin
CB
VGS
CB CB
RFout
CB
/4
Figure 8-41 Schematic of the designed 7 GHz amplifier including the PCB substrate de-scription and the S-parameter simulation setup.
RR1R = 5.90 kOhm
RR2R = 5.11 kOhm
CC2C = 270 pF
CC4C = 270 pF
CC3C = 270 pF
CC1 C = 270 pF
MLINTL1Subst = “MSub1”W = 43.4 milL = 254.9 mil
MLINTL3Subst = “MSub1”W = 43.4 milL = 254.9 mil
MLINTL4Subst = “MSub1”W = 43.4 milL = 191 mil
V_DCSRC 1 Vdc = 5.0 V
VIAFCV1D = 15.0 milH = 20.0 milT = 0.5 mil
VIAFCV3D = 15.0 milH = 20.0 milT = 0.5 mil
VIAFCV4D = 15.0 milH = 20.0 milT = 0.5 mil
S-PARAMETERSMSub
S_ParamSP1Start = 0.1 GHzStop = 10 GHzStep = 0.01 GHzCalcNoise = yas
MSUBMSub1H = 20.0 milEr = 3.48Mur = 1Cond = 5.8E + 7T = 1.4 milTanD = 0.0031
MLOCTL2Subst = "MSub1"W = 43.4 milL = 199 mil
MLOCTL5Subst = "MSub1"W = 43.4 milL = 169 mil
Display Templatedistemp2“S_Params_Quad_dB_Smith”“S_21_11_wZoom”
DispTemp
Display Templatedistemp3 “Circles_Ga_NF”“Circles_Stability”
DispTemp
ATF551M4X1
ATF551M4
G S2
S1 D
VIAFCV2 D = 15.0 milH = 20.0 milT = 0.5 mil
TermTerm 1Num = 1Z = 50 Ohm
+
–
RR3 R = 20 kOhm
RR4R = 100 Ohm
ap_pnp_2N3906_19930601Q1
ap_pnp_2N3906_19930601Q2
+
–
TermTerm 2Num = 2Z = 50 Ohm
+
–
OPTIONS
OptionsOptions 1Temp = 16.85 Tnom = 25 Topology check = yesV_RelTol = 1e-6l_RelTol = 1e-6GiveAllWarnings = yesMaxWarnings = 10
Figure 8-42 Simulated S-parameters of 7 GHz amplifier.
Input Reflection Coefficient
Output Reflection Coefficient
Reverse Transmission, dB
Forward Transmission, dB
m2
freq = 7.000 GHz
S(1, 1) = 0.079 / –172.251
impedance = Z0 * (0.855 – j0.018)
0
6.0 6.5 7.0 7.5 8.0
0 1 2 3 4 5 6 7 8 9 10
dB
(S(1
, 1))
dB
(S(2
, 1))
dB
(S(2
, 2))
dB
(S(1
, 2))
–5
30
20
10
0
–10
–20
–30
–40
–50
–60
freq, GHz
6.0 6.5 7.0 7.5 8.0
freq, GHz
freq, GHz
0 1 2 3 4 5 6 7 8 9 10
freq, GHz
–10
–10
–20
–30
–40
–50
–60
–70
–15
–20
0
–10
–20
–30
–40
–25
m2
S(1
, 1)
S(2
, 2)
freq(100.0 MHz to 10.00 GHz)
freq(100.0 MHz to 10.00 GHz)
m5
m4
m3
m3
freq = 7.000 GHz
S(2, 2) = 0.023 / 93.824
impedance = Z0 * (0.996 + j0.045)
m5
freq = 7.000 GHz
dB(S(1, 2)) = –17.928
m4
freq = 7.000 GHz
dB(S(2, 1)) = 13.777
freq[690] S[690](1, 1) S[690](1, 2) S[690](2, 1) S[690](2, 2)
0.023 / 93.8244.885 / –129.2860.127 / –143.7300.079 / –172.2517.000 GHz
