Notes on noise figure measurement and deembedding device noise figure from lossy input network

Transcription

1 Notes on noise figure measurement and deembeddg device noise figure from lossy put network Bill lade May, 00 Introduction This brief note reviews the Y-factor method of establishg noise figure and the effects of unmatched put networks on the measurement of device noise figure (i.e. de-embeddg the device noise figure from that of the put network, as long as put network losses are not too large). ally, a brief look at characterisg an put balun for de-embeddg a differential device put is given. This method is not suitable for frequencies above GHz or so because we rely on placg standard low-tolerance MD components as reference loads. Above -3GHz, parasitics and placement errors will domate the measurement results. or a quick-and-dirty noise measurement L or low- band usg a balun, the results may be sufficient for your needs. Explanation of Y-factor method Consider the system igure. igure : Noisy two-port showg put calibrated noise source and load (measurg device). If we consider the system to be matched for the noise source both on and off states, we assume the power put to the system for the noise-source off state will be the 90K thermal noise off ktb

2 and the on power to be related to the thermal noise through the designated Excess Noise Ratio (ENR) by on ktb( ENR ). The two port network is assumed to have ga G and noise figure (generally unknown at this pot). Usg the additional assumption that the two-port network ga is much larger than the noise figure of the power meter (usually a spectrum analyzer). This means the noise figure of the measurg device does not have a significant impact on the measurement itself (otherwise, the noise contribution of the measurg strument needs to be determed so its contribution can be removed). Given that many receivers have gas of the order of 60dB or more, spectrum analyzer noise figure is likely to be significant comparison (5-30dB is possible). Usg our power equations, the measured power on the output with the noise source the off state is out off GkTB, where is the unknown noise figure, k is Boltzmann s constant, T is room temperature (90K) and B is the measurement bandwidth. With the source switched on, we have on G( ENR ) ktb ( GkTB. out ) This can be rearranged as on GkTB( ENR ). out ormg the ratio of noise source on output power to noise source off output power yields Y out off ENR out on. olvg for the noise figure yields ENR. Y One can also solve for the ga of the two-port network: G Y Y ktb out on. Annex : What happens unmatched cascaded noisy networks? To answer this, consider the system igure : an put network and the device, whose noise figure we wish to establish.

3 igure : Illustration of cascaded networks that are not necessarily matched. pecifically, the first two-port network represents the put network that comes before the (possibly differential) LNA put of the receiver module (i.e. MA connectors, microstrip transmission les, baluns, etc.). This network is assumed passive, so it will suffer some sertion loss that will contribute to the overall system noise and reduction of ga. The reflection coefficients dicated igure are based on a reference impedance (usually 50 ohms). M and M represent the terstage mismatch factors that vary between 0 and, if the terface is completely reflective or completely matched, respectively. As shown, these quantities are given by M 00R 50 Z and M 4R R ( )( ). Z Z The variables R, R, R, Z, Z are the equivalent put resistance, first stage output resistance, equivalent put resistance, first stage output impedance and put impedance, respectively. We will contue to normalize everythg to 50 ohms by means of the reflection coefficients and parameters. Resistances and impedances are mentioned here only to show the lk with the usual circuit parameters. The noise figures of stages and, respectively, are and. ollowg the analysis [], if we attach a 50 ohm load at 90K to the put of the system, we can measure an output noise power given by G pg sys M ktb, out where we call sys the system noise figure (measured by the Y-factor method). In terms of the noise contributed by the put, first and second stages, the output noise power can be written as G pg M ktb GM ( ktb. out ) The first term of this expression gives the noise contributed by the 90K source as well as the ternally

4 generated noise referenced to the put of the first stage. The second term gives the contribution of the second () stage to the measured noise at the output, referenced to the put of the second stage. The mismatch factors are necessary because they modify the ga of the stages (by puttg the power ga terms of available put power, i.e. transducer ga). This is because the power ga is defed terms of full cident power, and not the power that actually works (i.e. is transmitted) to drive the stage. Equatg the two precedg expressions and solvg for sys yields M sys ( ). M G p If the first stage is fully passive, the noise figure will be proportional to the loss L, such that the noise figure of the put network is L, where and are stage measured -parameters. implifyg, we get the noise figure of the passive put network:, which reduces to the reciprocal of the network ga matched situations. The power ga of stage unmatched circumstances can be computed as G p. Knowg the parameters of the put network and the reflection coefficient at the put reference plane of stage (the receiver module) and the full system noise figure, the noise figure can be extracted usg sys G p M M. In terms of reflection and parameter quantities, this means

5 sys. If the source feedg tage is defed as 50 ohms, then. This means sys It is terestg that this expression no longer has any dependence on or form as the expression for the unmatched cascade noise figure found [].. This is the same Reviewg the assumptions and required quantities:. ource is assumed matched to 50 ohms;. irst stage (put network) is passive, i.e. is equivalent to the sertion loss of tage ; 3. sys is measured usg Y-method ection 5; 4. Need to measure, and of the put network to compute tage sertion loss and de-embeddg factor for the noise figure. Annex 3: parameters of the put balun Many modern R devices rely on differential (balanced) R puts to mimise couplg to other circuit elements. This requires the use of an put balun, or balanced-unbalanced transformer, because antenna feeds are typically unbalanced transmission systems. or this reason, a method to extract the -parameters of the balun is needed. In order to extract the put network parameters, three reflection coefficient measurements are needed usg three known termations. It is convenient to use a. network termated with short circuit;. termated with matched load; 3. termated with known mismatch (capacitor, for example). The open circuit would be convenient, but the effects of field frgg at the open microstrip ends can troduce uncertaty the measurement, particularly as frequency creases above GHz. Note that the measurement setup described here is for use with situ balun measurements without any special connections. urface mount components are used. This measurement should yield useful values for balun -parameters for frequencies up to -3GHz or so. Above this and component placement errors and parasitics will troduce errors. Moreover, we ignore scatterg to the common mode. This will troduce some error, but if the common-mode rejection of the R device under test is more than 0dB or so, the error will be small and the power scattered to the common mode by the balun will appear as either return loss or sertion loss, addg to the noise on the put. However, for a quick-anddirty measurement on a system CB without special calibration/de-embeddg structures (like TRL), this method can be useful. igure 3 shows a block diagram of the measurement setup.

6 igure 3: Illustration of measurement setup for extractg equivalent parameters of put network. The network analyzer connection is unbalanced (sgle-ended) whereas the loads need to be applied to a balanced le. ce the signals of terest to many microwave receiver ICs are balanced (differential), the common mode should always be matched. Any power scattered to the common mode by the baluns should appear as loss to the system, and hence will contribute to system noise and ga values (this is what

7 actually happens operation). If the balun output is perfectly balanced, the common-mode loadg will have no effect. Note that measurement 3 must clude the loadg of the 50 ohm resistors differential mode ( Z d parallel with 00 ohms). This analysis is still somewhat approximate because the even and odd-mode characteristic impedances of the dual microstrip feedle will not be the same because of terle couplg. Usg the expression for put reflection coefficient L L with three different load reflection coefficients, we can extract the parameters measurg the put reflect with a network analyzer. hort circuit: L Matched load: L 0 s. m. Known mismatch: L c x Usg the fact that the put circuit is reciprocal, we know that. We can then solve for the three unknown parameters, viz. c c m m x / c s m x s m s References [] R. E. Coll, oundations of Microwave Engeerg, econd edition, IEEE ress, 00. [] J. M. Collantes, R. D. ollard and M. ayed, Effects of DUT mismatch on the noise figure characterization: a comparative analysis of two Y-actor techniques, IEEE Trans. Instrumentation Meas., vol. 5, no.6, Dec. 00, pp