Common-source cold-fet used to validate noise figure measurements and on-wafer FET noise parameters

Transcription

1 INTRUMENTION Revista Mexicana de Física 59 (03) NOVEMBER-DECEMBER 03 Common-source cold-fet used to validate noise figure measurements on-wafer FET noise parameters B. E. Figueroa Reséndiz, M. C. Maya Sánchez, J. A. Reynoso Hernández Centro de Investigación Científica y de Educación Superior de Ensenada, División de Física Aplicada, Departamento de Electrónica y Telecomunicaciones, Carretera Ensenada-Tijuana No. 398, Zona Playitas, 860, Ensenada, B.C. México. [email protected]; [email protected]; [email protected] Received October 0; accepted 5 July 03 This work proposes the use of a common-source cold-fet with gate forward biased to validate the noise figure measurements the noise parameters of on-wafer transistors. Since a common-source cold-fet behaves as an attenuator, its noise figure noise parameters can be determined from S-parameters measurements. Three methods for determining the noise parameters of the common-source cold-fet are investigated. The first one uses the noise correlation matrix for passive devices (the S-parameters), the second one is the tuner method the third one is the F 50 method. The noise figure measured the noise figure computed from S-parameters agree quite well. The noise parameters extracted with the tuner method the F 50 method show good correlation with the noise parameters computed with the S-parameters. These results validate both the noise figure measurements the noise parameters extraction. Keywords: Noise figure; noise parameters; cold-fet; source-pull tuner method; F 50 method. PACS: De; 06.0.fb; Dc. Introduction Noise figure is one of the receiver parameters; that indicates its ability to process low-level signals. This figure of merit is mainly dictated by the low noise amplifier (LNA), it depends on the transistors noise parameters [,]. The knowledge of noise figure at different input impedances allows the determination of the four noise parameters (NPs) [3]: minimum noise figure, F min, noise resistance R n, the magnitude phase of the optimum reflection coefficient, Γ opt (or the real the imaginary parts of optimum admittance, Y opt= G opt +jb opt ). The NPs depend on both the frequency the bias po. The transistor NPs can be determined by using either the multiple-impedance technique (tuner method) [4-8] or the F 50 method [9,0]. The tuner method uses measures of noise figure at different impedances presented at the input of the device under test (DUT). This technique can be applied to any two-port device. The F 50 method requires the knowledge of the transistor noise model, only needs measurements of the transistor noise figure when its input is loaded with a broadb load near 50 ohms. To minimize errors in the noise parameters extraction the F 50 method uses frequency redundancy. Therefore, errors in the measurements of noise figure reflection coefficient preclude the correct determination of the NPs. Therefore, high reliable measurements of noise figure reflection coefficients are required. In this sense, noise verification stards are also sought after in order to validate the noise figure measurements of mismatched devices. The common-gate cold-fet configuration has been proposed as a verification stard to check the accuracy of NPs [-]. The cold-fet in common-gate configuration can be used as a noise verification stard since its noise figure noise parameters can be directly computed from the device S-parameters. The common-gate cold-fet transistor behaves as a variable attenuator in function of the bias po, their noise parameters are the same order of magnitude as the active device ones. Besides, the common-gate cold-fet transistor can also be used to check the accuracy of the noise figure setup []. However, the common-gate cold-fet configuration is not a common on-wafer FET configuration its implementation requires additional technological steps. For example, a specific bonding to become the transistor in common-gate configuration or a specific foundry design, are needed. For on-wafer transistors, the commonsource is the most common configuration, therefore the implementation of the common-source cold-fet configuration is straightforward. Even though the common-source cold-fet exhibits a large noise figure (around 0 db) [], it can be used as noise verification stard, but not to check the accuracy of the noise figure setup (especially, when noise figure values less than db have to be measured). For these reasons, in this work a common-source cold-fet with gate forward biased is proposed to validate the noise figure measurements the noise parameters of on-wafer transistors only. Like the common-gate cold-fet, the common-source cold- FET exhibits mismatches close to an active device, therefore the noise figure measurements are performed in a similar condition. Furthermore, the performance of both the tuner method the F 50 method for determining the noise parameters in the frequency range of 5-0 GHz are validated using the common-source cold-fet as verification stard. It is important to comment that the common-source cold- FET configuration under reverse bias has been used as noise source [3-4]; but not as calibration element due to large

2 COMMON-SOURCE COLD-FET USED TO VALIDE NOISE FIGURE MEASUREMENTS AND ON-WAFER FET NOISE PARAMETERS 56 noise level. By contrast, the common-source cold-fet under the forward bias behaves as attenuator it can be used to verify noise figure measurements.. Noise figure noise parameters of the common-source cold-fet A common-source cold-fet configuration is proposed to validate the measured noise figure the noise parameters extracted by the F 50 tuner methods. The common-source cold-fet is implemented by using a common-source MES- FET biased with V GS >V bi >0 (V bi is the built-in voltage ) floating V DS (open drain). The procedure to obtain the noise parameters is described next... Computation of the passive device noise parameters using S-parameters Since the common-source cold-fet is a passive element, its noise figure is given by [5]: F = L, () where L are the device losses computed from the S- parameters. The available gain is G = /L. On the other h, the common-source cold-fet s noise parameters can also be computed from the S-parameters through the correlation matrices, as described as follows. For passive devices, the correlation matrix, in its chain representation C, is determined from [6,7] as C = kt a fp ZA { Z D + Z D } P ZA, () Where k denotes the Boltzmann s constant ( JK ), T 0 is the stard temperature (90 K) f is the incremental noise bwidth. The superscript denotes the conjugate transpose, T a is the room temperature (300 K), Z D is the device impedance matrix computed from its S-parameter measurements. Finally, P ZA is the transformation matrix from impedance to chain representation [7], given by P ZA = D Z Z D 0 Z D. (3) The noise parameters can be derived from C [,7], since C = [ C C C C ] = 4kT 0 f R n (F min ) R n Y opt (F min ) R n Y opt R n Y opt. (4) Then, from Eq. (4), the noise parameters are given as C R n = 4kT 0 f, (5) ( ( )) G opt = C Im C, (6) C B opt = Im ( C F min = + C ) C, (7) [ C + C Y kt 0 f opt]. (8) The asterisk denotes the complex conjugate... Determination of the noise parameters using the F 50 technique In the F 50 technique the noise parameters are determined from the knowledge of the device noise model from the measurements of its noise figure, at different frequencies, when a source admittance is connected to the input of the DUT [9-0]. The analysis of the noise equivalent circuit allows us to determine the correlation matrix, C [0,6], which models the whole noise transistor behavior. Then, from the knowledge of C the noise parameters are computed according to the procedure described next. It is important to comment that, to the author s knowledge, noise analysis of the common-source cold-fet applying the F 50 technique has not been reported yet. The active region of the transistor, biased as a cold-fet, is modeled as a Schottky diode in series with a channel resistance, whose impedance is denoted as Z, shown in Fig. (a). The small-signal equivalent circuit of the commonsource cold-fet is shown in Fig. (b) [8], where the noise sources are also included. The parasitic elements (R g, R d, R s, L g, L d, L s ) are bias independent, while the active region modeled by Z is bias dependent. The parasitic elements of the equivalent circuit are extracted according to the method described by Reynoso et al. [8]. Once the parasitic elements are known, then Z is de-embedded. The noise sources of the rinsic transistor are represented as noise source voltages e gs e ds, where the former is associated to the gate-source terminal the later is associated to the drain-source terminal. The rinsic noise sources e gs e ds are arranged o the correlation matrix

3 56 B. E. FIGUEROA RESÉNDIZ, M. C. MAYA SÁNCHEZ, AND J. A. REYNOSO HERNÁNDEZ where A G is the ABCD matrix of the gate network, A GiS is the ABCD matrix of the gate- rinsic-source networks P ZAiS is the transformation matrix from the impedance to chain representation of the rinsic-source networks [7]. This matrix is given by P ZAiS = is Z Z is 0 Z is, () where Z is is the impedance matrix of the rinsic transistor in series with the source network. Equation () can be expressed as C = C AEXT +C AINT, (3) with C AEXT = A GiS C AD ( A GiS) +A G P ZAiS C ZS ( A G P ZAiS) +C AG (4) FIGURE. Common-source cold-fet: (a) Equivalent circuit for the rinsic transistor. Note: α g α are the factors related to the gate-source current distribution, to the gate-drain current distribution, respectively. At low current values, α g =/3 α =/. R ch is the channel resistance, n is the ideality factor q is the electron charge. (b) Total electrical equivalent circuit, divided in networks including noise sources. denoted as C Z. The noise contribution of the parasitic elements is modeled by means of the noise source voltages e Rg, e Rd e Rs, associated to the gate, the drain the source parasitic resistances, respectively. To obtain the total correlation matrix, the equivalent circuit is divided o four networks, as shows in Fig. (b). To model the noise contribution of the rinsic transistor, the impedance matrix representation C Z is given by: C Z = e gs e gs e ds = e gs e gs e ds [ C C C C ]. (9) Next, the correlation matrix associated to the source network, C ZS, is added to C Z : C ZiS = C Z +C ZS, (0) ( ) where C ZS = kt 0 f Z S + Z S, Z S being the impedance matrix of the source network. Then, the matrix C ZiS is transformed to the chain representation the gate drain noise contribution represented by the C AG C AD correlations matrix are added. Therefore, the correlation matrix C is defined as C = A GiS C AD ( A GiS) +A G P ZAiS C Z ( A G P ZAiS) +A G P ZAiS C ZS ( A G P ZAiS) +C AG, () C AINT = A G P ZAiS C Z ( A G P ZAiS). (5) The extrinsic noise correlation matrix, C AEXT, includes the whole effect of thermal noise associated to the extrinsic elements, this contribution can be determined as long as their values are known. The rinsic correlation matrix, C AINT, represents noise generated in the rinsic transistor. The contribution of the Schottky diode shot noise can also be included by adding a current source noise (i shot ) in parallel to the diode. The spectral density, i shot, can be determined from low frequency noise measurement, is considered as an extrinsic noise source [0]. According to the procedure described before (from Eq. (9) to ()), the total shot noise correlation matrix is given by: C shot = A G P ZAiS [ e shot Where e shot = Z did i shot, ] (A G P ZAiS). (6) Z did is the diode impedance (Z did = nkt0 i shot qi GS ), = qigs. Then, if the shot noise is included in the equivalent circuit, the shot noise correction matrix, C shot, should be added to the Eq. (4). In the same way, the Eq. () defines only the cold-fet thermal noise contribution (considering as passive device); if the shot noise is considered, C shot is added to Eq. (). The shot noise contribution in the noise figure will be discussed at the results section. It is important to comment that the cold-fet configuration can be represented by two Schottky diodes: one due to the gate-source contacts the other one due to the gatedrain contacts. Then, the C shot should be redefined considering the two shot current sources noise, one associated to the

4 COMMON-SOURCE COLD-FET USED TO VALIDE NOISE FIGURE MEASUREMENTS AND ON-WAFER FET NOISE PARAMETERS 563 gate-source Schottky diode (i shot GS ) the other one associated to the gate-drain Schottky diode (i shot GD ) [4]: C shot = A G P ZAiS Z H 0 [ ] i shot GS 0 (A G P ZAiS ) Z H 0 i 0. (7) shot GD Where i shot GS = qigs i shot GD = qigd, H 0 is the conversion matrix from an ishot GS ishot GD noisesource configuration to an admittance noise-source configuration [4], Z is the impedance of the rinsic device. However, since in this work the floating drain-source configuration is considered, I GD = 0 the Eq. (7) is reduced to (6). As mentioned early, since the common-source cold-fet is a passive device,c Z, therefore C AINT, can be determined from the knowledge of Z. Moreover, to validate the F 50 technique we assumed that the elements of C Z are unknown, they can be computed from the noise figure by using [6]: [ ] F =+ 4kT 0 Re (Z g ) f [ Z g] C, (8) Z g P = A G P ZAiS. () Since the C Z is an Hermitian matrix, Im(C ) = Im(C ) = 0, C = (C ) C = Re(C ) + jim ( C), Eq. (9) becomes where C i = [M i M i M i3 M i4 ] C Re(C Im(C M i = P + Z g i P ) ), () + Z g i P P + Z g ip P, (3) M i = P + Z g i P + Z g i P P + Z g ip P, (4) M i3 = Re(P P ) + Z g i Re(P P ) + Re(Z g i P P ) + Re(Z g ip P ) (5) where Z g is the impedance value of the load presented at the input of the DUT. The noise figure is measured for N f frequency pos. Substituting Eqs. (3) (5) o Eq. (8), it follow [ i = [ Z g i ] P C Z P Zg i with i=,.., N f,. i. Nf ], (9) i = 4kT 0 Re(Z g i ) f[f i ] [ ] [ Z g i ] C AEXT, (0) Z g i M i4 = Im(P P ) Z g i Im(P P ) Im (Z g i P P ) Im ( Z g ip P ). (6) Equation () has four unknowns, so at least four frequency pos are needed to solve the system. When N f > 4, the system is redundant. On the other h, the elements of C Z can be modeled by a frequency dependent L-order polynomial: C mn = L Cmnf l i l, (7) l=0 where Cmn refers to C, C, Re ( ) ( C or Im C ). When L=, substituting (7) o (), the following matrix equation results: M M f M M f M 3 M 3 f M 4 M 4 f = M i M i f M i M i f M i3 M i3 f M i4 M i4 f M Nf M Nf f Nf M Nf M Nf f Nf M Nf 3 M Nf 3 f Nf M Nf 4 M Nf 4 f Nf C 0 Re(C ) 0 (8) Re(C ) Im(C ) 0 Im(C ) Since Eq. (8) is not a square matrix, an analytical solution does not exist. To solve Eq. (8) a numerical optimization method is then required. The optimization s goal is to minimize the error function, ε F 50, defined as, C C 0 C

5 564 B. E. FIGUEROA RESÉNDIZ, M. C. MAYA SÁNCHEZ, AND J. A. REYNOSO HERNÁNDEZ ( ε F 50 = Nf (M i + M i f i ) C N f i= + (M i + M i f i ) C + (M i3 + M i3 f i ) Re(C ) + (M i4 + M i4 f i ) Im(C ) i ) /, (9) where i is computed from Eq. (0). The initial values are obtained as follow: C, 0 Re(C ) 0 Im(C ) 0 are computed applying the pseudo-inverse to (8), C 0 is determined from C 0 = 4kT a Re(Z (, )) [0], C, Re(C ), Im(C ) C are equal to zero. The optimization order is: C, 0 C, C, 0 C, Re(C ) 0, Re(C ), Im(C ) 0, Im(C ). This order has been established after observing how the variations of C Z elements affect the behavior of the noise parameters. Besides, the following restrictions are taken o account in the optimization process: C 0, C 0, 0 ρ = C C. (30) C Once C Z has been determined, the noise parameters are computed from C (see Eqs. (3)-(5) (5)-(8))..3. Determination of noise parameters applying the tuner technique In order to verify the correct extraction of the noise parameters we compare the results obtained with the proposed method with the results obtained using the tuner technique. Noise parameter extraction based on the tuner system uses the measure of the noise figure under different input admittances (at least seven different admittances). The noise parameters are determined from the solution of the noise figure equation defined as function of the noise parameters of the source admittance, which is given by [3,4] F (Y g j ) = F min + R n G g j [ (G g j G opt ) + (B g j B opt ) ], (3) where Y gj = G gj +B gj, with j=,..., N s, N s is the number of pos of Y g at which F is measured. Equation (3) can be rewritten, according with the Lane method [4], as: F (Γ g j ) = A + BG g j + C + B (B g j) + DB g j G g j, (3) where F min = A + 4BC D, (33) R n = B, (34) B opt = D B, (35) FIGURE. Noise figure measurement system.

6 COMMON-SOURCE COLD-FET USED TO VALIDE NOISE FIGURE MEASUREMENTS AND ON-WAFER FET NOISE PARAMETERS F IGURE 3. a) Noise figure b) noise parameters of the receiver. 565

7 566 B. E. FIGUEROA RESÉNDIZ, M. C. MAYA SÁNCHEZ, AND J. A. REYNOSO HERNÁNDEZ 4BC D G opt =. (36) B The A, B, C D parameters can be obtained by applying the least square method. 3. Experimental results 3.. Noise figure setup The S-parameters the noise figure of the device under test have been measured from 5 to 0 GHz using the experimental setup shown in Fig.. The setup consists of a vector network analyzer (VNA), a probe station, an input network a noise receiver. The VNA (HP850C) is used to measure the S-parameters of the device under test (DUT), the reflection coefficients of the source, the receiver the device input (denoted as Γ S, Γ R Γ in, respectively). The on-wafer probe station (SUMMIT-9000 from Cascade-Microtech) is used as a test fixture for inserting the DUT. The input network consists of one switch (SWT) to select the DUT input connection between the VNA or the tuner input, a tuner (focus iccmt-500-tc), the V GS bias-tee, a coplanar microwave probe for connecting the DUT input. The noise receiver consists of a spectrum analyzer (SA) (HP70000 series), a low-noise amplifier (LNA), one switch (SWT) to select the output DUT connection between the VNA or the LNA input, an isolator, the V DS bias-tee, a coplanar microwave probe for connecting the DUT output. All measurements are controlled with an external PC via GPIB Ethernet. Prior to measure the device noise figure, the system noise must be calibrated according to the procedure described in [9]. While the system noise calibration is performed, a thru is connected at the coplanar planes (- - ) instead of the DUT. A coaxial HP346C noise source (NS), connected at the 0-0 plane, is used to calibrate the noise system. In Fig. 3(a)-(b) the receiver s noise figure its noise parameters are reported. The noise figure is measured with the NS at cold-state [9]. It is important to mention that the isolator is used to avoid reflection between the DUT the noise receiver. A possible inconvenient of using an isolator is that the measurement frequency range is fixed by the operation frequency of the isolator. This is the reason why the noise figure measurements shown in Fig. 3(a)-(b) increase at frequencies greater than 9 GHz. 3.. Common-source cold-fet noise figure noise parameters An on-wafer MESFET, featured by a 0. µm gate-length a 60 µm gate-width, has been used in our investigation. The MESFET has been biased as common-source cold- FET, with floating drain, V GS = 0.76 V I GS =5 ma. According to the results reported by Reynoso et al. [8], the floating drain configuration overcomes the inconsistencies between DC RF techniques to extract the parasitic resistances the equations involves are an extension of those presented by Dambrine et al. [0]. From the measured S-parameters, shown in Fig. 4, it can be seen that the common-source cold-fet is a mismatched device (return loss > 0 db) with 4 db of transmission loss. FIGURE 4. S-parameters of the common-source cold-fet biased with V GS=0.76 V I GS=5 ma, measured (o) calculated ( ) using the equivalent circuit elements.

8 COMMON-SOURCE COLD-FET USED TO VALIDE NOISE FIGURE MEASUREMENTS AND ON-WAFER FET NOISE PARAMETERS 567 TABLE I. Equivalent circuit elements of the common-source cold- FET, biased with V GS=0.76V I GS=5mA R g (Ω) 3.47 L g (ph) R s (Ω) 9.9 L s (ph) 3.34 R d (Ω).85 L d (ph) Ideality factor (n).8 The elements value of the equivalent circuit, are extracted according to the method described by Reynoso et al. [8], are given in Table I. In Fig. 4 the S-parameters measured calculated using the equivalent circuit are compared good correlation is observed. Theoretical values of the common-source cold-fet noise figure have been computed by applying Eq. (). The noise parameters have been extracted with both the F 50 the tuner techniques. To apply the tuner method, different admittance values (N s >7) have been used to reduce the measurements errors [4-8]. To verify the noise figure measurements, the experimental common-source cold-fet noise figure is compared with the noise figure predicted by Eq. (), the comparison is reported in Fig. 5. The noise figure has been measured under matched input admittance ( 50Ω) condition. The theoretical noise figure shows a small ripple which is produced by mismatches of the DUT input. At frequencies lower than 8 GHz, the measured noise figure shows a good agreement with the theoretical results. Due to the isolator performance, at higher frequencies the experimental noise figure exhibits a ripple whose value oscillates around ± db. This ripple fixes the accuracy of the measurements. In order to investigate the shot noise contribution in the noise figure of the common-source cold-fet, C is calculated including the shot noise contribution as follow: C = kt a fp ZA { Z D + Z D } P ZA + A G P ZAiS [ e shot ] (A G P ZAiS). (37) The results of the noise figure calculated with (8) by using () (37), respectively, are reported in Fig. 5. The noise figure calculated including the contribution of shot noise is identical to the noise figure calculated considering only the thermal contribution. Both results agree with the noise figure calculated by using S-parameters. The F 50 method was applied considering only the thermal noise contribution, since the shot noise does not have a significant effect on the noise figure. In Fig. 6 are reported the values of the rinsic correlation matrix (C Z ) computed by using the F 50 method they are compared to experimental { data calculated from Z (C Z = kt a f Z + Z }). It is important to comment that Z is determined after performing a deembedding of the parasitic elements to the impedance matrix, FIGURE 5. Noise figure of a common-source cold-fet (biased with V GS=0.76 V I GS=5 ma): measured ( ), calculated by using S parameters (Eq. ()) ( ), calculated by using C without shot noise (Eq. ()) (x), with shot noise (Eq. (37)) (o). Z D (obtained from measurements of S-parameters). Notice that the values of C Z determined from F 50 method predict the experimental data of C Z calculated by using the measured S-parameters. Noise parameters determined with the F 50, the tuner technique the computed from the correlation matrix C (Eqs. ()-(8)) are reported in Fig. 7. It is observed that the noise parameters computed by F 50 are similar to those predicted by the S-parameters. On the other h, the noise parameters extracted with the tuner technique show a ripple. The ripple in F min is ±0.5 db at frequencies lower than 9 GHz the ripple becomes larger as the frequency increases. The ripple in R n is ±3Ω at frequencies lower than 8 GHz, increases at higher frequencies. The ripple in the phase of the optimum reflection coefficient is ±3 degrees. It is important to mention that the mean values of the noise parameters extracted with the tuner method are in good agreement with both the calculated value using S-parameters the computed value using F 50. According to the results, we can conclude that the tuner technique is more sensible to measurement errors than the F 50 technique. Noise figure has also been determined from the noise parameters extracted with both the F 50 technique the tuner technique. The results are plotted in Fig. 8. Furthermore, a comparison of the noise figure computed from the S parameters (Eq. ()) with those determined from the noise parameters is also reported in Fig. 8. It should be noticed that the noise figure determined with the tuner the F 50 methods agree quite well with the noise figure computed from the S-parameters up to 8 GHz. At higher frequencies the tuner results show a significant ripple, which is associated to the experimental noise figure, as mentioned before.

9 568 B. E. FIGUEROA RESE NDIZ, M. C. MAYA SA NCHEZ, AND J. A. REYNOSO HERNA NDEZ F IGURE 6. Elements of the rinsic correlation matrix: ( ) computed from F50 by using (o) the S-parameters. F IGURE 7. Common-source cold-fet s noise parameters: theoretical (computed from the S parameters ( )) extracted with the F50 ( ), tuner (o) techniques. The cold-fet has been biased with VGS =0.76 V IGS =5 ma.

10 COMMON-SOURCE COLD-FET USED TO VALIDE NOISE FIGURE MEASUREMENTS AND ON-WAFER FET NOISE PARAMETERS 569 FIGURE 8. Noise figure of the common-source cold-fet (biased with V GS=0.76 V I GS=5 ma): computed from the S parameters (Eq. ()) ( ), by applying the results of the noise parameters determined with the F 50 ( ) the tuner (o) techniques. The S-parameters of a common-source cold-fet have been used to validate the noise figure measurements the extraction of noise parameters of on-wafer devices. Since the common-source cold-fet behaves as a passive device, its noise figure noise parameters can be directly computed from its S-parameters. The experimental noise parameters have been extracted using the tuner F 50 methods. A good correlation between the measured calculated noise figure of the common-source cold-fet is observed. Similarly, the experimental noise parameters agree with the noise parameters computed with the S-parameters. Furthermore, the shot noise contribution on the common-source cold-fet noise figure has been investigated. Our results indicate that the shot noise contribution is not significant. Finally, these results demonstrate that the common-source cold-fet can be used to validate the noise figure measurements on-wafer transistor noise parameters extraction. 4. Conclusions. F. Daneville, IEEE Microwave Magazine (00) M.W. Pospieszalski, IEEE Microwave Magazine, (00) IRE Subcommittee on Noise, Proc. IRE 48 (960) R.Q. Lane, Proc. IEEE 57 (969) M. Mitama, H. Katoh, IEEE Trans. Microwave Theory Tech. 7 (979) J. M. O Callaghan J.P. Mondal, IEEE Trans. Microwave Theory Tech. 39 (99) G. Vasilescu, G. Alquie, M. Krim, Electron. Letters 5 (989) A. Boudiaf, M. Laporte, J. Dangla, G. Vernet. IEEE MTT-S Int. Microwave Symp. Dig. (99) P.J. Tasker, W. Reinert, B. Hughes, J. Braunstein, M. Schlechtweg, IEEE MTT-S Digest (993) A. Lázaro, L. Pradell J. O Callaghan, IEEE Trans. Microwave Theory Tech. 47 (999) L. Escotte, R. Olana, J. Rayssac, O. Llopis, J. Graffeuil, Electron. Letters 7 (99) L. Escotte, R. Plana, J. Graffeuil, IEEE Trans. Microwave Theory Tech. 4 (993) M.C. Maya, A. Lazaro, L. Pradell, Cold-FET ENR characterisation applied to the measurement of on-wafer transistor noise parameters, (3 nd European EUMC Microwave Conference, 00) pp M.C. Maya, A.Lazaro, L. Pradell, Microwave Optical Technology Letters, 40 (004) R. Pettai, Noise in receiving systems, (John Wiley Sons, Inc. 984). pp H. Hillbr, P.H. Russer, IEEE Trans. Circuits Systems, CAS-3 (976), pp J. A. Dobrowolsky, Introduction to Computer Methods for Microwave Circuit Analysis Design, (Artech House, Inc. st Edition, Boston, 99) pp J.A. Reynoso-Hernández, F.E. Rangel-Patiño, J. Perdomo, IEEE Trans. Microwave Theory Tech. 44 (996) A. Lázaro, M.C. Maya, L. Pradell, Microwave Journal 45 (00) G. Dambrine, A. Cappy, F. Heliodore, E. Playez, IEEE Trans. Microwave Theory Tech., 36 (988) 5-59.