320 SINGLE-TONE INTERMODULATION DISTORTION SUPPRESSION
Boe D jmj[ υ4 υ2 C ˛ υ3 C υ2 C ˇ υ4 υ3 ]
Beo D jmj[ υ4 C υ2 C ˛ υ3 υ2 ˇ υ4 C υ3 ]
BIF D Boo m D 1
The ˛ and ˇ represent the isolation in the LO and RF transformers resulting from their imbalance. The imbalance is illustrated in Fig. H.1 which is the same as used in Fig. 11.5 except the diode numbering convention has been made here to conform to that used in [1].
LO isolation D 20 log 1 ˛
RF isolation D 20 log 1 ˇ
The values for υ are a measure of the inequality of the forward voltages across the diodes:
υ2 D
V2
υ3 D
V1
V3
υ4 D
V1
V4
V1
Under ideal conditions
˛ D ˇ D υ2 D υ3 D υ4 D 1
Typical values for isolation by the transformers are 10 to 15 dB, while the values for υ range from 0.85 to 1.15.
VL
+
–
V1
V4
+
–
+
fp
VR
– β VR
–
+
–
V 2 –
+ V 3
–α V L
f0
f1
FIGURE H.1 Double-balanced mixer with transformer and diode imbalance.
SINGLE-TONE INTERMODULATION DISTORTION SUPPRESSION
321
The equations have been implemented in a program called IMPSUP, which determines the single-tone intermodulation suppression for a given set of frequency harmonics of the RF signal and LO oscillator, the relative RF signal and LO power levels, the peak value of the LO voltage, imbalances resulting in finite isolation in the transformers, and imbalances in the diode forward voltage drops. A sample run of IMSUP shows the intermodulation suppression for a variety of frequency harmonics:
LO and RF Signal Transformer Isolation (typ. 10 to 15 dB)
10.,10.
Ring diode voltage ratios: V2/V1, V3/V1, V4/V1 = ? Typically .85 to 1.15 (ideally =1)
0.85, 0.90, 1.15
Difference in LO and RF power in dB (typ. -20.)
-20.
Peak LO voltage = ?
3.
Forward diode saturation voltage (typ. 0.1) IM product n x FL +- m x Frf: n,m = ?
1, 1
For intermodulation product n x m = 1 1 IM Suppression = 0.000000E+00 dBc
New n,m values only? <Y/N> y
IM product n x FL +- m x Frf: n,m = ?
2, 1
For intermodulation product n x m = 2 1 IM Suppression = -0.437641E+02 dBc
New n,m values only? <Y/N> y
IM product n x FL +- m x Frf: n,m = ?
3, 1
For intermodulation product n x m = 3 1 IM Suppression = -0.954243E+01 dBc
New n,m values only? <Y/N> y
IM product n x FL +- m x Frf: n,m = ?
3, 2
For intermodulation product n x m = 3 2 IM Suppression = -0.602423E+02 dBc
New n,m values only? <Y/N> n
Completely new mixer specs? <Y/N> n
fin
322 SINGLE-TONE INTERMODULATION DISTORTION SUPPRESSION
REFERENCES
1. B. C. Henederson, “Reliably Predict Mixer IM Suppression,” Microwaves RF , Vol. 22, pp. 63–66, 68–70, 132, 1983. Also reprinted in RF and Microwave Designer’s Handbook , Watkins-Johnson, 1997–98 Catalog.
Radio Frequency Circuit Design . W. Alan Davis, Krishna Agarwal
Copyright 2001 John Wiley & Sons, Inc.
Print ISBN 0-471-35052-4 Electronic ISBN 0-471-20068-9
Index
ABCD matrix, see ABCD parameters ABCD parameters, 30, 53–56, 58, 74,
154 Active filter, 84 Active load, 13
Actual noise figure, 151
Admittance parameters, see y parameters AM, 3, 4
Ampere’s` law, 67, 69 AMPS, 278
ASITIC, 27 Available gain, 122
B-ISDN, 279 Balun(s), 115–118
Bandwidth efficiency, 1 Bandwidth, 35, 47, 159, 178, 280 Barkhausen criterion, 195, 197, 201 Beat note, 252, 259–261, 263, 271 Black body radiation, 145 Bluetooth, 283
Boltzmann probability, 145 Butterworth, 89–90, 92, 95–97
Capacitance fringing, 29–30
Capacitor resonances, 17 alumina, 16 BaTiO3 , 16–17
coupled microstrip, 26 hybrid, 14–15, 20 interdigital, 18
loss, 15–19
metal — insulator — metal, 18 monolithic, 14, 17, 20
NPO, 16–17 Porcelain, 16–17
Capacity, 3, 5–7 Cascaded amplifiers, 161 Cauer extraction, 97 CDMA, 3, 279–280, 282 Channel, 4
Characteristic admittance, 154 Characteristic impedance, 61–62, 65, 67,
72–73, 77–78, 102–103, 106, 114, 119–120, 154, 205, 289, 294, 306, 309
CHEBY, 102
Chebyshev, 90–92, 94–96, 98, 102 Circuit Q, 33, 44
Class A amplifier(s), 3, 122, 168, 181 Class A power amplifier(s), 139 Class AB amplifier(s), 3
Class B amplifier(s), 169–171, 173, 175–177, 181
Class C amplifier(s), 3, 178–179, 181–183, 188
Class D amplifier, 184
Class F amplifier, 185–186, 188 Coaxial transmission line, 67–68, 115 Collector efficiency, 185 Combiner(s), 117–118
Combining, power 141–142 COMSAT, 283
Conduction angle, 169, 170, 178–179, 183–184
Conductivity, 9–10 Conductor loss, 70–71, 73
Conversion compression, 227, 242
324 INDEX
Conversion gain, 243
Conversion loss, 226
Convolution, 225–226
Curvilinear squares, 12
Cutoff frequency, 85
Damping factor, see Damping ratio Damping ratio, 247, 250, 265–267, 269,
276
Darlington method, 99 Darlington procedure, 95, 97, 103 DBLTUNE, 49, 290
DCS, 278
DECT, 279 Dependent states, 6
Dielectric loss, 69, 71, 73 Discontinuities, 309, 311, 313 Divider(s), 117
frequency, 251, 255, 259
Double tuned circuit, 45–47, 290–291 DSB, see Noise
DSP, 279, 283
Dynamic range, 144, 227, 230, 242–243
Effective dielectric constant, 71–73, 289 Efficiency, 122, 139, 141, 162, 164,
168–169, 176–178, 180–185, 217, 218
multistage amplifier, 163 power added, 189, 191
ELLIPTIC, 94 Elliptic filter, 94
Error voltage, 254, 261 Even mode voltage, 28–29 Even-mode current, 106 Exchangeable gain, 122
FCC, 278, 282
FDMA, 3, 280
Feed-forward amplifier(s), 191–192 Feedback, 129, 136–138, 161, 191,
195–197, 200, 202, 206, 209, 247, 250, 261, 263
Filter(s)
all pass, 86–87, 94
bandpass, 86–87, 89, 101–102 bandstop, 86–87, 89, 101 high pass, 86–87, 89, 100 ideal, 85, 89
low pass, 85–87, 89, 94–95, 100–102, 228, 258, 262
low pass prototype, 89–90, 92–93, 99–101
Final value theorem, 259 Flow graph, 125
FM, 3
Fourier transform, 225–226, 232 Fractional bandwidth, 101–102 Friis formula, 162–163, 281 FSK, 279
Fukui equations, 161 Fukui noise model, 158
g parameters, 52, 74, 132, 197, 292 Generators, harmonic, 216
GMSK, 279
GPRS, 282
Group delay, 85–86 Group velocity, 62 GSM, 278, 282
h parameters, 51, 74, 132, 197, 292 HALO, 283
Harmonic generators, see Multiplier(s) Hybrid coupler, 118
Ideal transformer, 46–47, 105, 306 Image frequency, 224, 244–245 Image impedance, 54–57, 59 Image propagation constant, 57–58 Impedance match(ing), 36, 95, 141
Impedance parameters, see z parameters Impedance transformation, 105, 121 Impedance transformer, 120
IMSUP, 240, 319, 321 IMT-2000, 279
Indefinite admittance matrix, 78–79, 207, 298
Indefinite scattering matrix, 80, 82 Inductor(s)
circular spiral, 26 ferrite(s), 22–23 microstrip, 26 monolithic, 26 proximity effect, 22 self resonance, 21 spiral, 26–28, 30, 286 loss, 20, 22
Information, 1, 3–7 Injection locking range, 216 Input intercept point, 227 Insertion gain, 122 INTEL-SAT, 283
Intercept point input, 227, 242 output, 227
Third-order, 242, 281
Intermodulation distortion, 139, 191, 235 Third-order, 227, 241–242
Two-tone, 240 suppression, 230
Inverse Cheybyshev, 92–94 IP, 279
ISDN, 278
Isolation, 227–228, 235, 320–321
L circuit, 37–40
Ladder network(s), 88–89, 97 Laplace Transform, 255, 257 LMDS, 280
LO drive power, 227 Loop bandwidth, 250
Loop filter(s), 249–250, 254, 260–261, 264–265, 268–269, 276
Loop gain, 261–262, 265 Loss tangent, 16–17 Loss, conversion, 230
Manley-Rowe relations, 217 Mason’s nontouching loop rules, 125 Maximum gain, 129
Maxwell equation(s), 66, 74 Microstrip, 26, 71–72, 115 MICSTP, 73
Minimum phase, 88–89 Minimum transconductance, 201 Mixer(s), 247
active, 235 class 1, 235 class 2, 235 class 3, 236
double-balanced, 227, 230, 232, 234–237, 274, 319
ring, 230–231
single balanced, 227–230, 232 single-ended, 227
star, 230–232 Modulation, 1 Modulator, 239
Multiplier(s), 216, 218, 247, 256 Gilbert cell, 236–240
MULTIPLY, 218–219
Nagaoka correction factor, 24 Natural frequency, 266–267, 269
INDEX 325
Negative resistance, 204 NMT, 278
Noise figure, 122, 151–154, 157,
161–162, 164–165, 227, 243–244 double-sideband, 244, 246 single-sideband, 243–246
Noise measure, 152
Noise temperature, 151–152, 243–244 Noise, 1, 155, 191–192, 201, 204,
210, 230 flicker, 3, 144 Johnson, 144
minimum, 201, 203 Nyquist, 144
shot, 148–149 spot, 151
Nyquist formula, 147, 149, 151
Odd mode voltage, 28–29 Odd-mode current, 106–107 Ohmic contact, 13
Op-amp, see Operational amplifier(s) Open loop gain, 201, 262
Operational amplifier(s), 247–249, 254, 258–259, 262, 267, 272
Oscillator(s) Armstrong, 197–198
Clapp-Gouriet, 197–199
Colpitts, 197–200, 202 Hartley, 197–198, 202–203 injection-locked, 214 Pierce, 197–198
Vackar, 197–199
voltage controlled, 199, 206, 249–254, 256, 259–264, 270–272, 275
circuit, 39–41, 45 PACS, 279
Parallel plate line, 66 PARCONV, 292, 294
Phase detector(s), 247, 249, 250–254, 259–264, 271–272, 274–275
flip-flop, 272–273 sampling, 270–272 Phase error, 257–259
Phase margin, 247, 250 Phase velocity, 62 PLMR, 278
POLY, 97 Positive real, 96
Power amplifier(s), 3, 141, 191, 281 Power gain, 122
326 INDEX
Probability, 6–7, 146
PSTN, 278
QPSK, 279, 281
Reflection coefficient, 62–63, 74–75, 77–78, 96–98, 114, 129, 204–205, 207–209, 296
Resistor diffused, 10 metal film, 11
Resonant frequency, 35–36, 37 Response time, 247, 250 Return loss, 114
Rollett criteria, 132
S parameter(s), 74, 77, 115, 124–126, 128–129, 132, 136, 138, 206–209, 292, 294–296, 298–299, 306–308
Saturated resistor, 14
Scattering matrix, see S parameter(s) Scattering parameters, see S parameter(s) Schottky barrier, 13, 222, 233
SDR, 279 Selectivity, 85
Series — series, 51, 52, 197 Series — shunt, 51–52 Shockley diode equation, 173 Shunt — series, 52–53
Shunt — shunt, 51, 200–201 Signal-to-noise ratio, 151, 243 Skin depth, 21–22
Smith chart, 63–64, 131–133, 164 SOC, 283
SOLENOID, 23, 26, 285 Solenoid, 23, 285
parasitic capacitance, 25 Q, 25–26
SPARC, 209
Spectral regrowth, 281 Spurious voltages, 230 SSB, see Noise
SSB, see Noise figure, single-sideband Stability, 122, 129–134, 136–138, 141,
198 amplifier, 205 factor, 206 Kurokawa, 213 oscillator, 210 temperature, 173
Sum frequency, 224
T circuit, 41–42, 45 TACS, 278
Tapped C, see Tapped capacitor Tapped capacitor, 42–45 TDMA, 3, 278, 280, 282
TDR, see Time domain reflectometer Telegrapher’s equation(s), 59–61, 63,
65–66
Temperature coefficient, 11, 74 Thompson-Bessel, 93, 96
Time domain reflectometer, 305–306, 308, 313
Transducer power gain, 89, 123–124, 126, 243
Transient(s), 204, 210, 247, 264 Transmission coefficient, 74, 77–78 Transmission line equation, 61, 63 Transmission line(s), 59–62, 65–66, 71,
106–116, 118–121, 132, 305, 310 Two-wire line, 65–66
Type 1 PLL, 254, 259, 262, 265, 267, 276 Type 2 PLL, 254, 262, 265, 267, 270,
275
Type 3 PLL, 262
UHF, 278
Unilateral
amplifiers, 162, 164 approximation, 164 power gain, 126–127
Unloaded Q, 36
VCO, see Oscillator(s)
Voltage coefficient, 11
Wilkinson divider, 120
y matrix, see y parameters
y parameters, 51, 53, 74, 78, 132,
136–138, 197, 200, 207, 292, 294,
298
Y factor, 152–153
z parameters, 51–54, 56, 74, 123, 132, 197, 292, 294
16QAM, 281 1G, 282
2G, 282
3G, 279, 282 4G, 279 64QAM, 281
Radio Frequency Circuit Design . W. Alan Davis, Krishna Agarwal
Copyright 2001 John Wiley & Sons, Inc.
Print ISBN 0-471-35052-4 Electronic ISBN 0-471-20068-9
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