A new method to simultaneously determine the complete Tee and hybrid Pi equivalent circuit parameters of the SiGe HBT including parasitic intrinsic base resistance, is presented. This approach employs analytically derived expressions and is based on the analysis of measured scattering parameters over an adequate frequency range. This paper shows that a one-to-one correspondence exists between Tee and Pi topologies and very good fit between measured and simulated scattering parameters in the frequency range between 0.05 to 50 GHz is obtained

García, J.A.

Mediavilla, A.

Pérez-Vega, C.

Tazón, A.

Zamanillo, J.M.

English

AMS Acta

   A STRAIGHTFORWARD METHOD FOR DETERMINING SiGe HBTs INTRINSIC ELEMENTS OF HIBRID PI AND TEE SMALL-SIGNAL CIRCUIT MODELS FOR MULTIBIAS OPERATION  J.M. Zamanillo,  J.A. García, A. Mediavilla, A. Tazón and C.Pérez-Vega University of Cantabria - Communications Engineering Department (DICOM) Av. de los Castros s/n. 39005, Santander, Spain Phone +34-942-201391 ext. 13, Fax +34-942-201488, E-mail: zama@dicom.unican.es  ABSTRACT  A new method to simultaneously determine the complete Tee and hybrid Pi equivalent circuit parameters of the SiGe HBT including parasitic intrinsic base resistance, is presented. This approach employs analytically derived expressions and is based on the analysis of measured scattering parameters over an adequate frequency range. This paper shows that a one-to-one correspondence exists between Tee and Pi topologies and very good fit between measured and simulated scattering parameters in the frequency range between 0.05 to 50 GHz is obtained.  INTRODUCTION  Different ways to extract small-signal microwave equivalent circuits of HBT devices from measured data have been proposed in the past. Most of the models that dealt with small signal HBT device performance make use of the Tee model topology, like Wei et al [1], because all the model parameters can be directly tied to the physics of the device. It is not clear which of the two topologies is better to characterize SiGe HBT transistors. This paper demonstrates that a one-to-one correspondence exists between Tee and hybrid Pi models; however some of the Pi model parameters exhibit frequency dependence with respect to the Tee model parameters. This behavior has also been observed in GaAs devices by Teeter and Curtice [2], therefore, it is necessary to optimize the electrical components for both topologies.  In this work a direct comparison between HBT small signal Tee and Pi models is made, taking into account the intrinsic base resistor and feedback capacitors as intrinsic elements (their value varies with bias), splitting the intrinsic part in two: approximate and complete. From the approximate part it is possible to compute the Pi topology of the device using analytical expressions previously developed by us [3], [4]. Tee topology is now computed using a new set of expressions based on the fact that a one-to-one correspondence exists between the two circuit topologies. However, slight variations in Pi model parameters become noticeable at high frequencies. For the devices investigated by us, this effect occurs above 30-40 GHz.  METHODOLOGY FOR THE EXTRACTION OF THE HYBRID PI AND TEE SMALL-SIGNAL MODELS.  Using the techniques previously developed by our group [5], [6], it is possible to compute the parasitic elements from scattering parameter measurements either, at cut-off, DC, or by an optimization process at several bias points. The circuit topology used to determine the parasitic elements is shown in Fig 1(a), and, in our case, cut-off measurements up to 40 GHz were performed. A conventional de-embedding process extracts the intrinsic scattering matrix of the HBT (4), (5). Due to the fact that the complete intrinsic HBT model proposed in this work (Fig 1(b)) has 10 elements, and using the real and imaginary parts of the scattering parameters there are only 8 equations. Therefore, it is necessary to use analytical equations to obtain the intrinsic elements of simplified models as shown in (Fig 1(c) and Fig 1(d)) for both topologies.      This method allows to properly compute the values of Cbepi, Rbepi, Rbcpi, Cbcpi, gm, Taupi,  Rcepi and Ccepi for Pi topology, and Cbet, Rbet, Rbct, Cbct, α0, fα, Tautee,  Rcet and Ccet for Tee topology. From these values, our approach computes Rbi and Cbcf for both models, using the following expressions:  323212112 1ZZZZYYZRbi +⋅−+=   (1)   ( ) ++−−⋅−=32323121ImZZZZRZYCbibcfω  (2)  Where Z2 and Z3 are given by:  bcbcbcCRjRZ⋅⋅⋅+=ω12  (3)  bebebeCRjRZ⋅⋅⋅+=ω13  (4)    B Cpbi Cpci Lb Lc Rbx Rc Cce Re Le INTRINSIC HBT C E  B FULL INTRINSIC HBT Tee or Pi Model C E Rbi Cbcf Approximate INTRINSIC  HBT Tee or Pi Model B Cbcpi Cbepi Ccepi Vi Im Rcepi INTRINSIC Pi model of HBT Rbcpi Rbepi C E  B Cbct Cbet Ccet Vi Ic Rcet INTRINSIC Tee model of HBT Rbct Rbet C E Ie  Fig. 1  Small-signal model for SiGe HBT devices.   (a) Parasitic elements.    (b) Complete intrinsic 10 element model. (c) Simplified Pi intrinsic HBT model.   (d) Simplified Tee intrinsic HBT model.  The relationships between the linear current source Im and the extracted parameters for the hybrid Pi model is giving by: imm VGI ⋅=  (5) (a) (b) (c) (d)     Where Pijmm egGωτ−⋅=  (6)  And for the linear current source Ic and the extracted parameters for the Tee model are given by:  α⋅= ec II  (7)  Where  ⋅+⋅=−αωτααffjTeeje10  (8)  Very good agreement between the complete (Tee and Pi) models and scattering measurements is observed for a six finger device at the bias point Ic= 15mA,Vce=1.5 V, as shown in Fig 2. A microphotograph of this device designated 67 by the Daimler-Chrysler foundry is shown in Fig. 2(d).     Fig. 2 Measured vs. Modeled [S] parameters (Full Tee and Pi models). (a) S11&S22        (b) S21         (c)S12.   (d) Microphotograph of a 67 device.  (a) (c) (b) (d)     CONCLUSIONS  A new technique for the simultaneous extraction of hybrid Pi and Tee topologies of the Daimler-Chrysler SiGe HBT devices, has been presented. Very good agreement for a 67 device between our model (Tee and Pi) and measurements has been observed in the frequency range from 0.05-50 GHz for all bias points studied. Direct comparison between the HBT small signal Tee model and hybrid Pi topology has been made and it is shown that a one-to-one correspondence exists between both topologies. Linear models extracted by this method for another devices have shown satisfactory agreement between measured and simulated data and allowed us to validate the model and encouraged us to use these models in new designs.  ACKNOWLEDGEMENTS  This work has been supported by European TMR project contract No. ERB FMRX-CT96-0050.  REFERENCES  [1] C. Wei, et al,“Direct Extraction of Equivalent Circuit Parameters for Heterojunction Bipolar Transistors” IEEE Transactions on MTT, Sept. 1995, pp 2035-2039. [2] Douglas A. Teeter & Walter R. Curtice, “Comparison of Hybrid Pi And Tee HBT Circuit Topologies and their Relationship to Large Signal Modeling” 1997 IEEE MTT-S , Vol.2. [3] J.M. Zamanillo, C. Navarro, J.P. Pascual, A. Mediavilla and F. Arcioni. “Direct Extraction Method of Multibias Small-Signal Equivalent Circuit Model for SiGe Heterojunction Bipolar Transistors”. Microwave Engineering Europe Aug/Sept 1998, pp 45-51 [4] J.M Zamanillo, A. Tazón, A. Mediavilla and C. Navarro et al. “Simple Algorithm Extracts SiGe HBT Parameters”, Microwaves & RF, October 1999, pp. 48-57 [5] J.M. Zamanillo, C. Navarro, J. A. García, A. Tazón and A. Mediavilla “Multibias Small-Signal Direct Extraction Method of Equivalent Circuit Model For SiGe Heterojunction Bipolar Transistors”. Proceedings of 7th International Conference on Microwave and High Frequency Heating, Valencia Sept. 1999. pp 395-398 [6] J.M. Zamanillo, C. Navarro, J. A. García and A. Mediavilla “Novel approach to determine SiGe HBTs Intrinsic and Parasitic elements of a Small-signal Circuits Models for Multibias Operation”. 7th International Symposium on Recent Advances in Microwave Technology (ISRAMT ´99), Málaga Dec. 1999. pp 130-133    

A straightforward method for determining SiGe HBTs intrinsic elements of hibrid PI and TEE small-signal circuit models for multibias operation

AMS Acta - Alm@DL - Università di Bologna

   
A STRAIGHTFORWARD METHOD FOR DETERMINING SiGe HBTs INTRINSIC 
ELEMENTS OF HIBRID PI AND TEE SMALL-SIGNAL CIRCUIT MODELS FOR 
MULTIBIAS OPERATION 
 
J.M. Zamanillo,  J.A. García, A. Mediavilla, A. Tazón and C.Pérez-Vega 
University of Cantabria - Communications Engineering Department (DICOM) 
Av. de los Castros s/n. 39005, Santander, Spain 
Phone +34-942-201391 ext. 13, Fax +34-942-201488, E-mail: zama@dicom.unican.es 
 
ABSTRACT 
 
A new method to simultaneously determine the complete Tee and hybrid Pi equivalent circuit 
parameters of the SiGe HBT including parasitic intrinsic base resistance, is presented. This 
approach employs analytically derived expressions and is based on the analysis of measured 
scattering parameters over an adequate frequency range. This paper shows that a one-to-one 
correspondence exists between Tee and Pi topologies and very good fit between measured and 
simulated scattering parameters in the frequency range between 0.05 to 50 GHz is obtained. 
 
INTRODUCTION 
 
Different ways to extract small-signal microwave equivalent circuits of HBT devices from measured 
data have been proposed in the past. Most of the models that dealt with small signal HBT device 
performance make use of the Tee model topology, like Wei et al [1], because all the model 
parameters can be directly tied to the physics of the device. It is not clear which of the two 
topologies is better to characterize SiGe HBT transistors. This paper demonstrates that a one-to-one 
correspondence exists between Tee and hybrid Pi models; however some of the Pi model 
parameters exhibit frequency dependence with respect to the Tee model parameters. This behavior 
has also been observed in GaAs devices by Teeter and Curtice [2], therefore, it is necessary to 
optimize the electrical components for both topologies. 
 
In this work a direct comparison between HBT small signal Tee and Pi models is made, taking into 
account the intrinsic base resistor and feedback capacitors as intrinsic elements (their value varies 
with bias), splitting the intrinsic part in two: approximate and complete. From the approximate part 
it is possible to compute the Pi topology of the device using analytical expressions previously 
developed by us [3], [4]. Tee topology is now computed using a new set of expressions based on the 
fact that a one-to-one correspondence exists between the two circuit topologies. However, slight 
variations in Pi model parameters become noticeable at high frequencies. For the devices 
investigated by us, this effect occurs above 30-40 GHz. 
 
METHODOLOGY FOR THE EXTRACTION OF THE HYBRID PI AND TEE SMALL-
SIGNAL MODELS. 
 
Using the techniques previously developed by our group [5], [6], it is possible to compute the 
parasitic elements from scattering parameter measurements either, at cut-off, DC, or by an 
optimization process at several bias points. The circuit topology used to determine the parasitic 
elements is shown in Fig 1(a), and, in our case, cut-off measurements up to 40 GHz were 
performed. A conventional de-embedding process extracts the intrinsic scattering matrix of the HBT 
(4), (5). Due to the fact that the complete intrinsic HBT model proposed in this work (Fig 1(b)) has 
10 elements, and using the real and imaginary parts of the scattering parameters there are only 8 
equations. Therefore, it is necessary to use analytical equations to obtain the intrinsic elements of 
simplified models as shown in (Fig 1(c) and Fig 1(d)) for both topologies.  
   
 
This method allows to properly compute the values of Cbepi, Rbepi, Rbcpi, Cbcpi, gm, Taupi,  Rcepi and Ccepi 
for Pi topology, and Cbet, Rbet, Rbct, Cbct, α0, fα, Tautee,  Rcet and Ccet for Tee topology. From these 
values, our approach computes Rbi and Cbcf for both models, using the following expressions: 
 
32
32
1211
2 1
ZZ
ZZ
YY
ZRbi +
⋅



−
+
=  
 
(1) 
 
 
( ) 






++
−−⋅−=
3232
3
12
1Im
ZZZZR
ZYC
bi
bcf
ω
 
 
(2) 
 
Where Z2 and Z3 are given by: 
 
bcbc
bc
CRj
RZ
⋅⋅⋅+
=
ω12
 
 
(3) 
 
bebe
be
CRj
RZ
⋅⋅⋅+
=
ω13
 
 
(4) 
 
 
 B 
Cpbi Cpci 
Lb Lc Rbx Rc 
Cce 
Re 
Le 
INTRINSIC 
HBT 
C 
E 
 
B 
FULL INTRINSIC HBT Tee or Pi Model
 
C 
E 
Rbi
 
Cbcf
 
Approximate INTRINSIC  
HBT Tee or Pi Model
 
B 
Cbcpi Cbepi Ccepi 
Vi Im Rcepi 
INTRINSIC Pi model of HBT 
Rbcpi 
Rbepi 
C 
E 
 
B 
Cbct 
Cbet Ccet Vi 
Ic 
Rcet 
INTRINSIC Tee model of HBT 
Rbct 
Rbet 
C 
E Ie 
 
Fig. 1  Small-signal model for SiGe HBT devices.  
 
(a) Parasitic elements.    (b) Complete intrinsic 10 element model. 
(c) Simplified Pi intrinsic HBT model.   (d) Simplified Tee intrinsic HBT model. 
 
The relationships between the linear current source Im and the extracted parameters for the hybrid Pi 
model is giving by: 
imm VGI ⋅=  (5) 
(a) 
(b) 
(c) (d) 
   
 Where 
Pij
mm egG
ωτ−
⋅=  (6) 
 
And for the linear current source Ic and the extracted parameters for the Tee model are given by: 
 
α⋅= ec II  (7) 
 Where  



⋅+
⋅
=
−
α
ωτα
α
f
fj
Teeje
1
0
 
 
(8) 
 
Very good agreement between the complete (Tee and Pi) models and scattering measurements is 
observed for a six finger device at the bias point Ic= 15mA,Vce=1.5 V, as shown in Fig 2. A 
microphotograph of this device designated 67 by the Daimler-Chrysler foundry is shown in Fig. 
2(d). 
 
 
 
 
Fig. 2 Measured vs. Modeled [S] parameters (Full Tee and Pi models). 
(a) S11&S22        (b) S21         (c)S12.   (d) Microphotograph of a 67 device.  
(a) 
(c) 
(b) 
(d) 
   
 
CONCLUSIONS 
 
A new technique for the simultaneous extraction of hybrid Pi and Tee topologies of the Daimler-
Chrysler SiGe HBT devices, has been presented. Very good agreement for a 67 device between our 
model (Tee and Pi) and measurements has been observed in the frequency range from 0.05-50 GHz 
for all bias points studied. Direct comparison between the HBT small signal Tee model and hybrid 
Pi topology has been made and it is shown that a one-to-one correspondence exists between both 
topologies. Linear models extracted by this method for another devices have shown satisfactory 
agreement between measured and simulated data and allowed us to validate the model and 
encouraged us to use these models in new designs. 
 
ACKNOWLEDGEMENTS 
 
This work has been supported by European TMR project contract No. ERB FMRX-CT96-0050. 
 
REFERENCES 
 
[1] C. Wei, et al,“Direct Extraction of Equivalent Circuit Parameters for Heterojunction Bipolar 
Transistors” IEEE Transactions on MTT, Sept. 1995, pp 2035-2039. 
[2] Douglas A. Teeter & Walter R. Curtice, “Comparison of Hybrid Pi And Tee HBT Circuit 
Topologies and their Relationship to Large Signal Modeling” 1997 IEEE MTT-S , Vol.2. 
[3] J.M. Zamanillo, C. Navarro, J.P. Pascual, A. Mediavilla and F. Arcioni. “Direct Extraction 
Method of Multibias Small-Signal Equivalent Circuit Model for SiGe Heterojunction Bipolar 
Transistors”. Microwave Engineering Europe Aug/Sept 1998, pp 45-51 
[4] J.M Zamanillo, A. Tazón, A. Mediavilla and C. Navarro et al. “Simple Algorithm Extracts SiGe 
HBT Parameters”, Microwaves & RF, October 1999, pp. 48-57 
[5] J.M. Zamanillo, C. Navarro, J. A. García, A. Tazón and A. Mediavilla “Multibias Small-Signal 
Direct Extraction Method of Equivalent Circuit Model For SiGe Heterojunction Bipolar 
Transistors”. Proceedings of 7th International Conference on Microwave and High Frequency 
Heating, Valencia Sept. 1999. pp 395-398 
[6] J.M. Zamanillo, C. Navarro, J. A. García and A. Mediavilla “Novel approach to determine SiGe 
HBTs Intrinsic and Parasitic elements of a Small-signal Circuits Models for Multibias Operation”. 
7th International Symposium on Recent Advances in Microwave Technology (ISRAMT ´99), 
Málaga Dec. 1999. pp 130-133 
  
 


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A straightforward method for determining SiGe HBTs intrinsic elements of hibrid PI and TEE small-signal circuit models for multibias operation

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