Considerations on the Measurement of Active Differential Devices Using Baluns Vadim Issakov1 , Maciej Wojnowski2 , Andreas Thiede1 , Volker Winkler3 , Marc Tiebout4 , and Werner Simb¨urger2 1
Dept. of High-Frequency Electronics, University of Paderborn, Warburgerstr. 100, D-33098 Paderborn, Germany Email:
[email protected] 2 Infineon Technologies AG, Am Campeon 1-12, D-85579 Neubiberg, Germany 3 EADS DE, Woerthstr. 85, D-89077 Ulm, Germany 4 Infineon Technologies Austria AG, Siemensstr. 2, A-9500 Villach
Abstract—The characterization of active differential devices requires a four-port vector network analyzer. Thus, it is a common practice to attach balanced-unbalanced (balun) circuits to convert between single-ended and differential signals and perform the measurement using a lower cost two-port vector network analyzer (VNA) or a spectrum analyzer. However, removing the impact of baluns is a challenge. This paper presents an analytical analysis of the back-to-back interconnection of the baluns and considers the common de-embedding technique Insertion Loss. This technique is commonly applied for two-port measurements of differential devices to remove the impact of the baluns. The applicability and accuracy of this approach is discussed. The analytical results have been verified on a differential Low-Noise-Amplifier (LNA) at 24 GHz realized in Infineon’s B7HF200 SiGe:C technology. It is measured directly using a four-port network analyzer and the results are compared with a measurement using baluns and a two-port network analyzer.
I. I NTRODUCTION Accurate measurement of differential devices at microwave and millimeter-wave frequencies is a challenge. Differential signalling becomes increasingly popular in active circuits due to superior noise immunity and ground bounce insensitivity. In order to characterize differential devices, the mixed-mode S-parameters theory has been formulated [1] and measurement techniques have been developed [2]. Due to cost considerations a commercial four-port or a true-differential VNA might not be easily available. Thus, techniques for measuring multiport devices using a two-port network analyzer have been developed [3]. Several publications focus particularly on the measurement of differential four-port devices, such as e.g. Low-Noise-Amplifiers or coupled transmission-lines. One common method is to measure the scattering parameters of two ports, while the other two ports are terminated, as proposed in [4]. This method has the disadvantage of complexity, redundancy in the interpretation of measurement results and time consumption. It requires performing a sequence of six measurements to obtain the sixteen single-ended S-parameters and to convert them into the modal representation. Another very common practical approach is to introduce balun devices that provide balanced-to-unbalanced transformation [5]. This approach is popular due to its simplicity, but has the disadvantage of introducing additional components that cannot be easily de-embedded. A set of analytical equations
for a particular case of a balun realized with a hybrid rat-race coupler has been derived in [6]. Baluns are introduced in a two-port measurement setup in order to provide differential excitation at one reference plane and to combine the differential signals at the other reference plane of the DUT. Thus, the measured S-parameters after de-embedding can be only referred to as the differential S-parameters of the DUT, without the possibility of insight into the actual modal composition. The back-to-back connection of baluns is usually required in order to account for their impact using common de-embedding techniques. The simplest widely used method to characterize a balun is the Insertion Loss technique. The insertion losses of a back-to-back interconnection of two baluns are measured and divided by two, as described in [5]. This approach has a moderate accuracy and provides only the amplitude information. However, it does not require a VNA and can be easily implemented using a spectrum analyzer. We show in this paper that the frequency characteristics of a circuit, de-embedded using Insertion Loss, might be distorted due to numerous contributions that cannot be easily accounted for. Further alternatives for characterization of baluns that could be considered are Thru [7] and Thru-Reflect-Line (TRL) [8] deembedding techniques. The first method uses a single backto-back measurement and requires very restricting assumptions leading to inaccuracy. The latter is a more advanced technique that requires two more standards. However, this approach has the disadvantage of data discontinuities at the band edges related to the physical length of the line standard. Furthermore, the de-embedded S-parameters are referenced to an unknown characteristic impedance of the reference planes. In this paper we present a generalized analytical analysis of the back-to-back baluns interconnection measurement setup and apply the results for error estimation of the Insertion Loss technique. The latter is widely used, but valid only under very restricting assumptions. Goal of this work is to investigate qualitatively the impact of the restricting assumptions. Additionally, the accuracy of the Insertion Loss technique is analyzed by characterizing a 24 GHz differential LNA in Infineon’s SiGe:C technology. The mixed-mode S-parameter of the amplifier have been measured directly on-wafer using a four-port VNA and compared to the de-embedded results of an on-board two-port measurement using baluns.
II. T HEORETICAL A NALYSIS The measurement setup of a differential device using a calibrated two-port vector network analyzer or a spectrum analyzer can be considered as a chain connection of networks, as shown in Fig. 1. The baluns A and A are considered to be the error networks. Our goal is to characterize the threeport error-boxes and to remove their impact from the measured results of the DUT in Fig. 1.
Balun A
Balun A’
DUT
Reference Plane A
Reference Plane B
Fig. 1.
Two-port measurement setup of a differential device using baluns.
the Insertion Loss method, Eq. (2) can be related to the Sparameters measured in a 50 Ω environment as follows 2 DUT 2 s˜21,dd ≈ |s21,meas | , 2 |s21,b2b |
(3)
where s˜DUT 21,dd is the de-embedded gain of the amplifier, s21,meas is the transmission S-parameter measured for the setup in Fig. 1 and s21,b2b is the transmission S-parameter of the backto-back setup described in Fig. 2. The following analysis provides analytical expressions for the S-parameters expected to be measured for the back-to-back connection of the baluns and for the DUT measurement with baluns. The derived expressions are compared with (3) and the error of gain de-embedding using Insertion Loss approach is evaluated. A. Back-to-Back Measurement
For simplicity of the analysis it has to be assumed that the balun A is the mirrored version of the balun A, and that the networks are uncoupled. Furthermore, for easier interpretation of the results the modal balun S-parameters are considered. Using these assumptions we shall derive the expected Sparameters of the back-to-back interconnection in Fig. 2. This setup is required by the widely used Insertion Loss technique in order to evaluate the balun characteristics. a1 Balun A
b1
Reference Plane A
Fig. 2.
a1d
a2d
b1d
b2d
a1c
a2c
b1c
b2c
a2 Balun A’
b2
Reference Plane B
Back-to-back balun interconnection setup.
The Insertion Loss technique can be implemented using a two-port VNA or by means of a spectrum analyzer. In this technique the balun’s insertion loss in decibel ILbln (dB) is obtained by measuring the total insertion loss of the backto-back interconnection in Fig. 2 in decibel ILb2b (dB) and dividing it by two [5] ILbln (dB) ≈
ILb2b (dB) . 2
(1)
For a particular case when the DUT is a differential ampli˜ DUT is given using the fier, its de-embedded differential gain G Insertion Loss method by ˜ DUT (dB) ≈ Gmeas (dB) − ILb2b (dB). G
(2)
where Gmeas (dB) is the measured differential gain in decibel of the setup in Fig. 1. Obviously, this expression is only valid under very restricting assumptions and when all the components are matched to 50 Ω. Thus, under the assumption of a good port matching, high reverse isolation and negligible mode-conversion, required by
Independent of realization, baluns are considered to be three-port devices. The conversion of nodal to modal parameters for three-port devices is given in [9]. Thus, the internal ports of the multiport setup describe the differential and common mode wave amplitudes. Considering reciprocity of passive baluns exists s1d = sd1 , s1c = sc1 and sdc = scd . Therefore, the S-parameters of a balun can be written as follows ⎤ ⎡ s11 s1d s1c Sbln = ⎣ s1d sdd sdc ⎦ , (4) s1c sdc scc where index 1 denotes the single-ended port, index d denotes the differential port and index c denotes the common-mode port. Following the Multiport Connection Method for evaluating circuit parameters of an arbitrarily interconnected network [10], [11], the rows and columns of the overall Sparameter matrix Sb2b are ordered so that the wave variables are separated into groups corresponding to the e external ports and i internally connected ports. Thus, the wave relation of the multiport network can be written as See Sei ae be = , (5) bi Sie Sii ai where be and ae are the waves at the e external ports and bi and ai are the waves at the i internal ports. For the given case the relation can be written explicitly as follows ⎤ ⎡ ⎤⎡ ⎤ ⎡ a1 s11 0 s1d s1c 0 b1 0 ⎢ ⎥ ⎢ b2 ⎥ ⎢ 0 s11 0 0 s1c s1d ⎥ ⎥ ⎢ ⎥ ⎢ a2 ⎥ ⎢ ⎢ ⎥ ⎢ b1d ⎥ ⎢ s1d 0 sdd sdc 0 0 ⎥ ⎢ a1d ⎥ ⎥ ⎢ ⎥, ⎢ ⎢ ⎥ ⎢ b1c ⎥ = ⎢ s1c 0 sdc scc 0 0 ⎥ ⎥ ⎢ ⎥ ⎢ a1c ⎥ ⎢ ⎣ ⎦ ⎣ b2c ⎦ ⎣ 0 s1c 0 0 scc sdc a2c ⎦ b2d 0 s1d 0 0 sdc sdd a2d (6) where a1 , a2 and b1 , b2 are the incident and reflected wave variables at the external ports, a1d , a1c , a2d , a2c and b1d , b1c , b2d , b2c are the incident and reflected wave variables at the internal ports of the multiport, as depicted in Fig. 2,
s12,b2b = s21,b2b =
1 − s2dc − s2cc s21d + 1 − s2dd − s2dc s21c + 2s1c sdc s1d (scc + sdd )
(sdd + 1) (scc + 1) − s2dc (scc − 1) (sdd − 1) − s2dc
(9)
s11,b2b = s22,b2b =
s11 s2cc − 1 s2dd − 1 + s2dc − 2sdd scc − 2 s2dc + s21c sdd s2dc + scc 1 − s2dd + s21d scc s2dc + sdd 1 − s2cc + 2s1d s1c sdc scc sdd − s2dc + 1
(sdd + 1) (scc + 1) − s2dc (scc − 1) (sdd − 1) − s2dc (10)
and s11 , s1d , s1c , sdd , sdc , scc are the S-parameters of the balun defined in (4). The interconnection of the internal ports is described by the matrix Γ, defined as bi = Γai . In our case it can be explicitly written as ⎤ ⎡ ⎤⎡ ⎤ ⎡ 0 0 0 1 a1d b1d ⎢ b1c ⎥ ⎢ 0 0 1 0 ⎥ ⎢ a1c ⎥ ⎥ ⎢ ⎥⎢ ⎥ ⎢ (7) ⎣ b2c ⎦ = ⎣ 0 1 0 0 ⎦ ⎣ a2c ⎦ . 1 0 0 0 b2d a2d
and Γ is the matrix describing the interconnection of the internal ports
The scattering matrix of the back-to-back setup is given by s11,b2b s12,b2b −1 Sb2b = = See + Sei (Γ − Sii ) Sie . (8) s21,b2b s11,b2b
The S-parameters of the DUT with index cc describe commonmode and dd differential mode reflection and transmission coefficients. The measured S-parameters of the DUT with the error-boxes Smeas are thus given by substituting (12) and (13) into (11). The resulting expressions are very lengthy, but can be considerably simplified by assuming that at the frequencies of interest the mode conversion of the balun is negligible sdc = 0. The de-embedded forward transmission parameter, corresponding to the differential gain of the amplifier, is thus given by
Substituting the matrices from (6) and (7) into (8) after some math we arrive at the expressions (9) and (10) for transmission and reflection S-parameters, respectively. As we observe, due to the complexity of the expressions it is not possible to isolate the S-parameters of a single balun without further simplification. This leads naturally to de-embedding inaccuracy. B. DUT Measurement Now we shall analyze the inherent inaccuracy of DUT deembedding due to implementation of baluns. Let us consider the DUT in Fig. 1 to be a differential amplifier. For simplicity we have to assume that the DUT has negligible mode conversion, which is usually desired for a differential amplifier or a symmetrical passive structure. We can apply again the Multiport Connection Method and write expected measured S-parameters of the setup in Fig. 1 as follows s11,meas s12,meas −1 = See + Sei (Γ − Sii ) Sie , Smeas = s21,meas s11,meas (11) where See , Sei , Sei and Sie are sub-matrices of the multiport matrix
⎡ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎢ ⎣
See Sie
Sei Sii
s11 0 0 s1c 0 s1d 0 0 0 0
0 s11 s1c 0 s1d 0 0 0 0 0
= 0 s1c scc 0 sdc 0 0 0 0 0
s1c 0 0 scc 0 sdc 0 0 0 0
0 s1d sdc 0 sdd 0 0 0 0 0
s1d 0 0 sdc 0 sdd 0 0 0 0
0 0 0 0 0 0
0 0 0 0 0 0
sDUT 11,dd sDUT 21,dd 0 0
sDUT 12,dd sDUT 22,dd 0 0
0 0 0 0 0 0 0 0
0 0 0 0 0 0 0 0
sDUT 11,cc sDUT 21,cc
sDUT 12,cc sDUT 22,cc
⎤ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎥ ⎦ (12)
⎡ 0 ⎢ 0 ⎢ 0 ⎢ ⎢ 0 Γ=⎢ ⎢ 0 ⎢ ⎢ 0 ⎣ 0 1
s21,meas ≈ sDUT 21,dd + sDUT 21,cc
0 0 0 0 0 0 1 0
0 0 0 0 0 1 0 0
0 0 0 0 1 0 0 0
DUT 1 − sDUT 11,dd + s22,dd
1−
sDUT 11,cc
+
sDUT 22,cc
0 0 0 1 0 0 0 0
0 0 1 0 0 0 0 0
0 1 0 0 0 0 0 0
1 0 0 0 0 0 0 0
⎤ ⎥ ⎥ ⎥ ⎥ ⎥. ⎥ ⎥ ⎥ ⎦
(13)
s2 1d DUT DUT DUT 2 sdd + sDUT 11,dd s22,dd − s12,dd s21,dd sdd
s21c . DUT DUT DUT 2 scc + sDUT 11,cc s22,cc − s12,cc s21,cc scc (14)
It can be easily shown that the first part of the expression corresponds to the differential s21 , expected to be measured if baluns are considered to be purely differential two-port networks. However, the second part of the expression shows that the common mode gain of the amplifier is transferred through the common-mode transmission parameter of the balun and distorts the de-embedded gain. Therefore, the common-mode properties of the differential DUT also affect the de-embedding accuracy when measured using a two-port VNA and baluns. C. Insertion Loss De-embedding Error The expressions for s21,b2b and s21,meas , given in (9) and (11), respectively, can be substituted into (3) to obtain the approximate de-embedding error of the Insertion Loss technique in decibel |s21,meas | ˜ , (15) (dB) ≈ GDUT − GDUT = 20 log |s21,b2b | · sDUT 21,dd 2
where GDUT = |s21,dd | is the actual gain of the DUT. As can be observed, the error depends both on the properties of the DUT and of the balun. In particular, the error also depends on the magnitude of the transmission S-parameter of
the amplifier sDUT 21,dd that has to be de-embedded. Additionally, it can be observed from (15) that error of 0 dB in magnitude is possible under very restricting conditions on the balun Sparameters sdc ≈ 0, s1c ≈ 0, sdd ≈ 0.
(16)
In practice, this usually requires that these parameters remain below −30 dB over the frequency range of interest [12]. Thus, the de-embedded frequency characteristics is usually deformed and cannot be reconstructed using the Insertion Loss method. Another observation can be made without any restricting requirements on the balun parameters, but on the DUT. Assuming that the characterized differential amplifier has a very good port matching to 50 Ω sDUT 11,dd ≈ 0, sDUT 22,dd ≈ 0,
A. Balun Characteristics In order to evaluate characteristics of a possible balun realization, two on-board test baluns, based on ratrace hybrid coupler, have been designed for the center frequency of 24 GHz. The balun A presented in Fig. 3(a) has been designed to be symmetrical and to offer good port isolation and matching. The balun B, in Fig. 3(b) was designed asymmetrically, thus having higher differential to common-mode conversion and worse port matching. One branch of the balun is wider than the other one. Furthermore, the width of the trace on the rat-race coupler circumference was designed to have an impedance of 82.7 Ω, unlike the required 70.7 Ω for a 50 Ω system.
(17)
a very good reverse isolation sDUT 12,dd ≈ 0,
(18)
and a very good common mode rejection sDUT 21,cc ≈ 0,
(19)
the measured transmission S-parameter of the setup in Fig. 1 simplifies to s21,meas ≈
s21d
· sDUT 21,dd .
(20)
Thus, only in the case of an ”ideal” de-embedded amplifier, the error in (15) does not depend on the magnitude of the transmission S-parameter sDUT 21,dd , but only on the modal Sparameters of the balun (dB) = s2 · (s + 1) (s + 1) − s2 · (s − 1) (s − 1) − s2 cc cc dd dd 1d dc dc 20 log . 1 − s2dc − s2cc s21d + 1 − s2dd − s2dc s21c + 2s1c sdc s1d (scc + sdd ) (21)
The above expression provides the lower bound of the deembedding accuracy. III. M EASUREMENT V ERIFICATION The above theoretical considerations have been verified in measurement and simulation. Firstly, two on-board test baluns have been designed, simulated and characterized and the deembedding inaccuracy for an ”ideal” differential DUT has been considered. Secondly, a low-noise amplifier has been used as a device under test (DUT). It has been characterized using a two-port VNA with baluns and using a four-port VNA directly. This allows to estimate the distortion of the de-embedded frequency characteristics due to introduction of baluns.
(a) Ideal balun A Fig. 3.
(b) Imperfect balun B
Design of two 24 GHz baluns.
A direct characterization of such three-port devices in measurement is not trivial, thus the structures have been accurately simulated using HFSS. As shown further, due to very careful modeling of the PCB materials and very dense meshing in HFSS, a very good match between measured and simulated results has been achieved. In order to obtain insight on the properties of the baluns and whether they fulfill the requirements in (16), the modal S-parameters have to be considered. The comparison of the simulated modal S-parameters is presented in Fig. 4. The mode-conversion parameters s1c and sdc of the balun A are well below −30 dB in the frequency range 22.5 − 26.5 GHz. As we can observe, the balun B has much higher modeconversion than balun A, and can be used as an example of a balun that does not fulfill the requirements in (16). The differential matching better than −20 dB in the vicinity of the center frequency, observed for the balun A, is a good practical value. However, worse matching further away from the center frequency may be responsible for higher de-embedding error at these frequencies. Additionally, Fig. 5 presents the phase difference at the output ports of the baluns in the vicinity of the center frequency. The balun B provides a phase difference at the output that deviates from 180◦ , whilst the balun A seems to be close enough to 180◦ at the center frequency. Obviously, an ideal
0
0
Balun A Balun B
-5
-5
-15
-15
-20
-20
-25
-25 5
10
15
20
25
Frequency (GHz)
30
35
-30 0
40
5
10
15
0
0
-5
-5
-10
-10
-20 -25
35
40
-20 -25 -30
-30
-35
Balun A Balun B
-35 5
10
15
20
25
Frequency (GHz)
30
35
Balun A Balun B
-40 -45 0
40
5
10
15
20
25
Frequency (GHz)
(c) s1c
30
35
40
(d) sdc
0
0 -5
-5
Fig. 6.
On-board test structure for balun de-embedding.
tion. Accurate four-port Short-Open-Load-Thru (SOLT) [15] calibration has been performed to set the reference planes at the ports of the structure. It has to be emphasized that a setup using coaxial connectors has been disregarded in this case due to higher inaccuracy and difficult repeatability. The back-to-back connection of balun A has been also simulated in HFSS and compared with the measured S-parameters of the test structure in Fig. 6. Further, the simulated modal S-parameters of balun A in Fig. 3(a) have been used in (9) and (10) to obtain the back-to-back S-parameters analytically. The comparison of the results is presented in Fig. 7.
-10
-10
sdd (dB)
scc (dB)
30
-15
-15
-15
-15
0
-20
-20 -25 0
25
(b) s1d
sdc (dB)
s1c (dB)
(a) s11
-40 0
20
Frequency (GHz)
Balun A Balun B
5
10
15
20
25
Frequency (GHz)
30
Balun A Balun B
-25 35
40
-30 0
5
10
15
20
25
Frequency (GHz)
(e) scc
30
35
-5 40
(f) sdd
Simulated modal S-parameters of the 24 GHz baluns.
Fig. 4.
s21,b2b (dB)
-30 0
Balun A Balun B
-10
s1d (dB)
s11 (dB)
-10
-15
180◦ out-phased signal at the differential input port of the DUT is desired to excite the differential mode only.
-20 0
180
Measured Simulated using HFSS Calculated using Eq.9 5
10
15
20
25
Frequency (GHz)
30
35
40
(a) Transmission parameter s21,b2b
175
0 170
-10 165
Balun A Balun B 160 23
Fig. 5.
23.5
24
Frequency (GHz)
24.5
25
Phase difference at the output ports of the baluns.
Fig. 6 presents a test board having a back-to-back interconnection of the balun A with its mirrored version A . This test structure is used for the Insertion Loss de-embedding of the balun and corresponds to the setup in Fig. 2. The structure has been characterized on-board using Cascade Microtech ACP probes up to 40 GHz with 200 µm pitch in GSG configura-
s11,b2b (dB)
Phase difference (deg)
-10
-20 -30 -40
Measured Simulated using HFSS Calculated using Eq.10
-50 -60 0
5
10
15
20
25
Frequency (GHz)
30
35
40
(b) Reflection parameter s11,b2b Fig. 7. Comparison of measured, simulated and analytically calculated Sparameters of the back-to-back setup.
As we can observe, a very good agreement of the simulated and measured results is obtained. Thus, the equations (9) and (10) have been verified. The comparison of a good balun A and a worse balun B allows to evaluate the error due to imperfect properties of a balun. The simulated S-parameters of both baluns have been used in (21) to estimate the error due to Insertion Loss deembedding of an ”ideal” amplifier, as presented in Fig. 8. 3 2.5 2
Balun A Balun B
H (dB)
1.5
Fig. 9. Chip micrograph of 24 GHz LNA (chip size 0.55 mm × 0.59 mm).
1 0.5 0 -0.5 -1 -1.5 -2 20
21
22
23
24
25
Frequency (GHz)
26
27
28
Fig. 8. Comparison of the Insertion Loss de-embedding error due to imperfect balun properties for an ”ideal” amplifier used as a DUT.
As we can observe, the better balun A has an error lower than 0.7 dB over the whole frequency range 20 − 28 GHz. The error bound of the balun B reaches a maximum of 2.9 dB at frequency of 26.2 GHz. This is due to the peaks in common-mode transmission s1c and mode-conversion sdc S-parameters shown in Fig. 4(c) and Fig. 4(d), respectively, reaching −15 dB at this frequency, whilst these parameters should remain below −30 dB. The error can also become negative, which means the measured insertion loss of a balun can be estimated lower than it actually is.
In order to evaluate the approach of measuring a differential circuit using a two-port network analyzer and applying the Insertion Loss technique, the LNA chip has been mounted on a PCB with baluns, as presented in Fig. 10. Furthermore, a chip realizing a Thru standard, depicted in Fig. 11, has been bonded on an additional similar board. The diced chips were thinned to 185 µm to keep the bondwire lengths short. The singleended to differential conversion has been realized on-board using hybrid ring rat-race coupler centered at 24 GHz, similar to the one shown in Fig. 3(a). In this case the termination at the isolation port has been omitted, since good matching below −15 dB has been observed without it.
B. DUT De-embedding The two-port measurement using baluns has been further analyzed by characterization of a 24 GHz differential Low-Noise-Amplifier (LNA), presented in [13]. The circuit is realized in Infineon’s B7HF200 SiGe:C technology with lithographic feature of 0.35 µm [14]. The annotated chip micrograph is presented in Fig. 9. The size of the chip including the pads is 0.55 mm × 0.59 mm. The direct measurement has been performed on-wafer using Cascade Microtech Infinity probes up to 40 GHz with 100 µm pitch in GSSG configuration. Agilent’s network analyzer E8364A with a multiport test set Z5623A up to 50 GHz has been used. Accurate four-port Short-Open-LoadThru (SOLT) [15] calibration has been performed to set the reference planes at the input and output of the LNA. The measured four-port nodal S-parameters have been converted into modal representation and the differential S-parameters are used as the reference for further comparison with the results obtained using baluns.
Fig. 10.
Test board for two-port characterization of the LNA.
The further measurements have been performed on-board using GSG configuration, similar to the described in the previous section. The error-box includes the balun, bondwires and a short on-chip microstrip line. Obviously, a minor inaccuracy might be added due asymmetry of the error-box because of uneasy repeatability of the bondwires. However, this inevitable inaccuracy of the described error network is minimal compared to a typical laboratory coaxial measurement setup, e.g. including off-the-shelf hybrid couplers. The Insertion Loss approach has been applied to estimate balun characteristics and to de-embed the magnitude of the
IV. C ONCLUSION
Fig. 11. On-chip Thru standard for back-to-back setup (chip size 0.55 mm × 0.4 mm).
DUT gain. The measured two-port S-parameters of the DUT s21,meas and of the back-to-back connection of the baluns s21,b2b have been used in (3) and compared with the directly measured results using a four-port VNA. The comparison of the magnitude of the differential transmission parameter of the LNA is presented in Fig. 12. 12 10 9
Gain (dB)
ACKNOWLEDGMENT The authors would like to thank Fraunhofer ENAS, Paderborn, Germany for providing the measurement equipment. We would also like to thank Dr. Herbert Knapp of Infineon Technologies AG, Munich, Germany for the helpful comments. This work was supported under the German BMBF funded project EMCpack/FASMZS 16SV3295. R EFERENCES
11
8 7 6 5 4 3
Measured using a four-port VNA
2
De-embedded using Insertion Loss Before de-embedding
1 0 20
Measurement of differential devices using a two-port VNA and baluns is considered. We have shown analytically that DUT parameters, obtained using the widely used Insertion Loss technique, cannot be determined accurately, unless either the balun or the DUT exhibits ideal characteristics. Furthermore, we have derived expressions for error estimation due to the Insertion Loss method that provide insight on the impact of balun and DUT properties on the de-embedding accuracy. The analytical results have been confirmed in measurement. S-parameters of an LNA have been measured directly using a four-port VNA and compared with those obtained from a two-port measurement implementing the Insertion Loss deembedding technique. The distorted frequency response of the de-embedded LNA gain corresponds to the theory.
21
22
Fig. 12.
23
24
25
Frequency (GHz)
26
27
28
LNA gain comparison.
As we can observe, there is a gain deviation and a minor frequency shift in the de-embedded gain characteristics. Furthermore, there is a shape deformation of the frequency characteristics of the LNA. An additional erroneous inflection point at 22 GHz is observed for the curve de-embedded using the Insertion Loss method. Similar behaviour has been observed in [16], where a CMOS 24 GHz LNA has been characterized on-board with hybrid rat-race baluns and compared with the simulated results. A maximum deviation of several decibel has been observed in Fig. 12 between the directly measured and de-embedded results. The gain deviation of 1 dB at the center frequency is due to a moderate input and output port matching of the LNA of −6 dB and −11 dB, respectively, and corresponds to (15).
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