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Polynomial Model of Blocker Effects on Small Signal Gain and Noise Figure for LNA/Mixer Devices Used in Wireless Receivers
Authors: William Domino, Nooshin Vakilian, & Darioush Agahi
(all currently
work for Skyworks Solutions, Inc.)
V_{o} = k_{1} V_{in} + k_{3} V_{in}^{3} (1)
Figure 1 Polynomial Compression Models
are enough to produce an adequate model. In all cases the use of the model must be stopped above the point where it strays from true saturation.
V_{o} = k_{1} V_{in} + k_{3} V_{in}^{3} + k_{5} V_{in}^{5} + k_{7} V_{in}^{7 } (2)
To obtain the nonlinear gain, the above equation is divided by the input voltage, which yields
Gain = k_{1} + k_{3} V_{in}^{2} + k_{5} V_{in}^{4} + k_{7} V_{in}^{6 } (3)
LSG = k_{1}  3/4 k_{3} (V_{Large})^{2} + 5/8 k_{5} (V_{Large})^{4 } (4)
SSG = k_{1}  3/2 k_{3} (V_{Large})^{ 2} + 15/8 k_{5} (V_{Large}^{ })^{4 } (5)
Figure 2 Small Signal Gain Compression with Coefficient K3 = .0025
Figure 3 Small Signal Gain Compression with Coefficient K3 = .0050
In the method to be described, the coefficients of the SSG compression are directly determined by measurement and curve fit, rather than assuming they keep the precise relationship with the LSG coefficients that is seen in eq. (4) and (5). The noise figure increase that occurs is also measured and related to the small signal gain.
Figure 4 Model for Blocker Effects
SSG = a_{0}  a_{2}(Blocker)^{2} + a_{4}(Blocker)^{4} (6)
NoiseFactor = n_{0}  n_{1}(SSG) + n_{2}(SSG)^{2} (7)
Actually the blocker causes the small signal gain to be reduced while the system noise increases, causing a composite degradation in the noise figure of the system. This is taken into account when the above equations are fit to actual measurements.
Finally, after the blocker itself sees some compression, the LO noise is reciprocally mixed onto it (refer to appendix B), and the noise at the blockerdesired frequency offset falls into the desired band. This noise is then summed in with the other contributors.
Figure 5 Test Setup
the HP8970B noise figure meter. The blocker generator is filtered so as not to emit noise in the desired band, and the LO generator is filtered so as not to emit noise that would mix with the blocker. Also, the IF output is filtered so the blocker does not hit the NF meter with excessive power. The combiner has isolators on either side of it. On the noise source side, the isolator protects the noise source from the blocker. On the blocker side, the isolator insures that the port sees 50W both inside and outside the passband of the blocker filter.
The gain and NF with no blocker is measured, then a blocker is applied and the measurement is repeated for different blocker amplitudes. The measurements are stopped once the blocker reaches the highest value expected in the GSM system, or once the noise figure degrades by more than about 68dB.
It should also be noted that the frequencies of the measured noise band and of the blocker need to be chosen to avoid mixer spurs. If the blocker is located on or near a loworder mixer spur, then the NF meter will register an incorrectly high measurement.
Figure 6 Small Signal Gain vs. Blocker Voltage
Figure 7 Noise Factor vs. Small Signal Gain
To find the composite C/N, the basic quantities of gain, noise figure, and P_{1dB} are required, as are the coefficients of the smallsignal gain polynomial (a0, a2, a4), and the noise factor polynomial (n0, n1, n2). We find the small signal gain and the noise figure based on the level of the blocker, and then add the reciprocally mixed LO phase noise at the end.
We must apply the large signal compression to the blocker itself, since in our model this compression occurs before the LO noise reciprocal mixing is applied. A polynomial with higher orders can be applied for the LSG just as for the SSG, but in our experience it is adequate to apply 3^{rd}order distortion only for the LSG, as long as the large signal does not go far beyond the P1dB point of the system. Therefore the LSG coefficients can be derived either in the same manner as the SSG coefficients, or they can be taken from the measured P_{1dB} and the relationship in eq. (4) where k5=0. Appendix C details the P_{1dB} derivation.
Figure 8 Example of Model's Prediction of C/N (click to enlarge)
What makes the approach powerful is that once the model is derived, in can be plugged into the chain calculations for a complete receiver. Then, various whatif analyses can be done with accurate results for any blocker level hitting the LNA/mixer. For example, the effect of different frontend SAW filters with different levels of stopband attenuation for outofband blockers can be checked, and an accurate tradeoff can be made between the SAW’s passband insertion loss and its stopband selectivity.
1) W. E. Sabin and E. O. Schoenike, “Single Sideband Systems and Circuits”, second edition, McGraw Hill, 1995
Figure B1 RX Input Signals, and LO with Phase Noise Spectrum
Figure B2 Signals Downconverted to IF, with Overlap of ReciprocallyMixed Noise
a = 4/3 { 10^{1/20 }  1 } (c6)
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