IEC 62761 Edition 1 0 2014 02 INTERNATIONAL STANDARD NORME INTERNATIONALE Guidelines for the measurement method of nonlinearity for surface acoustic wave (SAW) and bulk acoustic wave (BAW) devices in[.]
General terms
BAW duplexer antenna duplexer composed of RF BAW resonators
BAW filter filter characterised by a bulk acoustic wave which is usually generated by a pair of electrodes and propagates along a thin film thickness direction
BAW acoustic wave, propagating between the top and bottom surface of a piezoelectric structure and traversing the entire thickness of the piezoelectric bulk
Note 1 to entry: The wave is excited by metal electrodes attached to both sides of the piezoelectric layer
3.1.4 cut-off frequency frequency of the pass-band at which the relative attenuation reaches a specified value
3.1.5 duplexer device used in the frequency division duplex system, which enables the system to receive and transmit signal through a common antenna simultaneously
The FBAR thin film BAW resonator features a piezoelectric layer positioned between two electrode layers, with stress-free surfaces on the top and bottom This design is mechanically supported at the edges on a substrate that incorporates a cavity structure, as illustrated in Figure 1, or alternatively, a membrane structure.
Note 1 to entry: This note applies to the French language only
Receiver (Rx) band frequency band used in a receiver part to detect signals from an antenna
Rx filter filter used in a receiver part to eliminate unnecessary signals
Note 1 to entry: The Rx filter is a basic part of a duplexer
A SAW filter is defined by its use of one or more surface acoustic wave transmission lines or resonant elements Typically, the surface acoustic wave is generated by an interdigital transducer and travels along a substrate.
The SMR BAW resonator features a structure composed of an electrode/piezoelectric layer/electrode, supported by a series of thin films with alternating low and high acoustic impedance These quarter-wavelength layers function as acoustic reflectors, effectively decoupling the resonator from the substrate, as illustrated in Figure 2.
Note 1 to entry: This note applies to the French language only h
SAW acoustic wave, propagating along a surface of an elastic substrate, whose amplitude decays exponentially with substrate depth
3.1.12 transmitter (Tx) band frequency band used in a transmitter part to emit signals from an antenna
Tx filter filter used in a transmitter part to eliminate unnecessary signals It is a basic part of a duplexer
Response related terms
Insertion attenuation is defined as the logarithmic ratio of the power delivered to the load impedance prior to the insertion of the duplexer compared to the power delivered to the load impedance following the duplexer's insertion.
3.2.2 pass band band of frequencies in which the relative attenuation is equal to or less than a specified value
3.2.3 reflectivity dimensionless measure of the degree of mismatch between two impedances Z 1 and Z 2 , i.e.,
− , where Z 1 and Z 2 represent respectively the input and source impedance or the output and load impedance
Note 1 to entry: The absolute value of reflectivity is called the reflection coefficient
3.2.4 relative attenuation difference between the attenuation at a given frequency and the attenuation at the reference frequency
3.2.5 stop band band of frequencies in which the relative attenuation is equal to or greater than a specified value
3.2.6 transition band band of frequencies between the cut-off frequency and the nearest point of the adjacent stop band
Nonlinearity related terms
3.3.1 harmonics non-linear distortion of a device response characterized by the appearance of frequencies at the output equal to integral multiples of the original signal frequency
3.3.2 hysteresis memory effect phenomenon where the output is not determined only from the input and depends also on the internal state, in other words, the history of the input
IP power level where intensity of the non-linear signal generated by the intermodulation distortion (IMD) is equal to that of two input signals at the output
Note 1 to entry: This note applies to the French language only
IMD, or intermodulation distortion, refers to the non-linear distortion in a device's response, which results in the emergence of output frequencies that correspond to the differences or sums of integral multiples of two or more input frequencies.
Note 1 to entry: This note applies to the French language only
3.3.5 jammer signal incoming unnecessary signal
3.3.6 nonlinear distortion distortion of the signal waveform caused by nonlinearity of the system where the signal transmits
Note 1 to entry: When the distortion is originated to the frequency dependence of the system signal transfer function, it is called the linear distortion
3.3.7 one decibel compression point input power where gain, the ratio of the output to the input, decreases by 1 dB from the value when the input is very weak
3.3.8 saturation phenomenon where gain, the ratio of the output to the input, decreases and approaches to zero when the input is large
3.3.9 three tone test non-linearity measurement applying three sinusoidal signals with different frequencies simultaneously
3.3.10 triple beat test same as the three tone test
3.3.11 two tone test non-linearity measurement applying two sinusoidal signals with different frequencies simultaneously
4 Basic properties of nonlinear system
Behaviours of nonlinear system
Let us consider a response y(x) of a circuit or a device when a signal x is applied When the hysteresis (memory effect) is negligible or ignored, the Maclaurin expansion of y with respect to x gives
( x c x c x c x y (1) where c m is the expansion coefficient It should be noted that c m = 0 for even m, when the circuit/device satisfies y(− x) = − y(x)
In this scenario, we analyze the simultaneous application of two sinusoidal signals with frequencies \( f_a \) and \( f_b \), and amplitudes \( a_a \) and \( a_b \), where \( a_a \) significantly exceeds \( a_b \) The combined signal can be expressed as \( x = a_a \cos(2\pi f_a t) + a_b \cos(2\pi f_b t) \) Consequently, the resulting output \( y \) can be approximated based on this relationship.
Equation (2) illustrates the impact of nonlinearity on circuit or device output The first two terms reflect changes in the transmission coefficients for signals a and b, indicating saturation from large signal inputs, typically with c3/c1 being negative The second line's three terms represent harmonic generation at frequencies of the form f = mf_a, where m is an integer The two terms in the third line denote the creation of new signals at frequencies f = f_a ± f_b, known as second-order intermodulation distortion (IMD2) Lastly, the remaining two terms in the fourth line describe frequencies of the form f = |2f_a ± f_b| or f = |2f_b ± f_a|, referred to as third-order intermodulation distortion (IMD3).
In wireless communication, a receiver tuned to a specific frequency \( f_t \) can detect incident signals at frequencies \( f_t/2 \) and \( f_t/3 \) due to harmonic generation, potentially interfering with the main signal Additionally, when two signals \( f_a \) and \( f_b \) meet certain frequency relationships, such as \( f_t = |f_a \pm f_b| \) or \( |2f_a \pm f_b| \), intermodulation distortion (IMD) can produce signals at \( f_t \) that disrupt detection In frequency division duplex (FDD) systems, transmitting at frequency \( f_a \) alongside an incident signal \( f_b \) can lead to IMD that interferes with the main signal Furthermore, nonlinearity in transmitters can generate spurious emissions that affect other wireless communications These scenarios underscore the critical need to characterize and suppress the nonlinear behavior of RF systems and components.
The 1 dB compression point (P 1dB) is commonly used to characterize transmission compression, indicating the input signal level at which the transmission coefficient drops by 1 dB In contrast, the intercept point is utilized for intermodulation distortion (IMD) characterization, where the power of the IMD2 signal, denoted as P a±b, is defined for the frequency f = |f a ± f b |.
The equation \$P_{a \pm b} = \frac{P_{oa} P_{ob}}{OIP2}\$ applies when signal levels are significantly lower than saturation levels Here, \$P_{oa}\$ and \$P_{ob}\$ represent the output power at frequencies \$f_a\$ and \$f_b\$, respectively, while \$OIP2\$ denotes the output second-order intercept point This relationship can also be expressed in decibels for further analysis.
In Equation (3), all variables are expressed in dBm
Similarly, power P 2a ± b of the IMD3 signal with f = |2f a ± f b | is expressed as
The equation \$P_{2a \pm b} = \frac{P_{oa}^2 P_{ob}}{OIP3^2}\$ applies when signal levels are significantly lower than saturation levels In this context, OIP3 refers to the output third-order intercept point This relationship can also be expressed in decibels for further analysis.
In Equation (4), all variables are expressed in dBm
The intercept point is defined by the input signal level \( P_{ia} (= P_{ib}) \), resulting in \( P_{a \pm b} = OIP2 \) and \( P_{2a \pm b} = OIP3 \) The input second- and third-order intercept points, IIP2 and IIP3, are associated with OIP2 and OIP3, respectively.
IIP3 = OIP3 + IA (6) whereIA is the insertion attenuation in dB of the device measured with very weak input signal level
Figure 3 shows typical variation of P oa (n = 1), P a±b (n = 2) and P 2a±b (n = 3) with P ia (= P ib )
OIPn and IIPn can be graphically estimated by identifying the intersection points of two extrapolated linear lines In this scenario, IIP2 and IIP3 are approximately 25 dBm and 33 dBm, respectively, while OIP2 is also noted.
OIP3 are about 20 dBm and 28 dBm, respectively
Input signal power, P ia (=P ib ) (dBm)
O ut put s ignal pow er (dB m )
Figure 3 – Fundamental and harmonics output as a function of input signal power
Equation (2) shows that the 1 dB compression point (P 1dB) and the third-order intercept point (IIP3) are defined by the formulas \$10 \log[4(1-0.89) \frac{c_1}{c_3} R_0]\$ and \$10 \log[4 \frac{c_1}{c_3} R_0]\$, respectively, where \$R_0\$ represents the circuit impedance This leads to a significant relationship expressed in decibels.
The relationship described is not universally applicable, particularly in RF filters, due to the frequency-dependent nature of parameters c₁, c₂, and c₃ Additionally, nonlinear parameters like IIPn and OIPn are influenced by frequencies fₐ, f_b, and fₜ, necessitating their specification during the measurement of nonlinear signals generated in RF.
Measurement setup for nonlinearity
Harmonics measurement
Figure 4 illustrates a fundamental configuration for measuring the N-th harmonics of RF components or systems A signal generator (SG) provides a sinusoidal signal with frequency \$f_a\$ and power \$P_{ia}\$ to the device under test (DUT), while a target spectrum component \$P_t\$ at frequency \$f_t\$ is also analyzed.
The spectrum analyser (SA) selectively detects the frequency \$f_a\$, and during measurement, we will address two key issues: the negligible nonlinearity of both the signal generator (SG) and the SA, and the well-defined circuit impedance from the device under test (DUT) ports for both the fundamental frequency \$f_a\$ and its harmonics \$f = n f_a\$ (where \$n \leq N\$) This is particularly crucial for passive RF filters, as their frequency selectivity relies on impedance mismatching with surrounding circuits, making the device characteristics sensitive to circuit impedance Typically, the circuit impedance is set to match the specific impedance \$R_0\$ of the measurement system.
1 RF BAW devices are often called the film bulk acoustic resonators (FBARs) or solidly mounted resonators
(SMRs) depending their device configuration e s
Figure 4 – Basic setup for the harmonics measurement
An appropriate filter is essential for eliminating nonlinear signals produced in the peripheral circuit, as illustrated in Figure 5 However, passive filters only demonstrate the circuit impedance of R0 within their pass band, necessitating the addition of an attenuator (ATT) between the filter and the device under test (DUT) When the ATT has a nominal attenuation of A dB, its insertion enhances the return attenuation of the peripheral circuit as observed from port 1 by 2A dB.
The insertion of the ATT leads to a decrease in input signal intensity by A dB, which subsequently reduces the intensity of the n-th harmonics by nA dB This reduction in signal level may introduce fluctuations in the SA read due to thermal noise To address this issue, increasing the SG output appears to be a viable solution However, it is essential to verify (a) whether the harmonics generated in the SG are negligible for the measurement and (b) whether the heating of the ATT causes any time-dependent variations in the attenuation level.
The ATT inserted between the DUT and SA is aimed at suppressing harmonics generation at
SA and variation of the input admittance of SA Of course this ATT is not necessary when these effects are negligible
Figure 5 – Practical setup for the harmonics measurement
When the output power of the signal generator (SG) is inadequate, a power amplifier (PA) must be added, but inserting a filter may not be feasible due to the need for higher output power to counteract the attenuation caused by the inserted attenuator (ATT), which can exacerbate the PA's nonlinearity Instead, an isolator or circulator is typically used to mitigate the impact of the input impedance from the device under test (DUT) port 1 on the PA It is important to note that while isolators and circulators can transmit spurious signals, measures must be taken to sufficiently suppress their generation within the PA Additionally, since these components generally operate effectively within a limited frequency range, incorporating an ATT may be necessary to enhance the return attenuation observed from the DUT port.
Figure 6 – Setup when the circulator/isolator is used
IMD Measurement
Figure 7 shows two configurations for the IMD measurement of RF components or systems
The two-tone test involves applying two sinusoidal signals with frequencies \$f_a\$ and \$f_b\$ to the Device Under Test (DUT) using two signal generators (SGs) A target spectrum component \$P_t\$ at frequency \$f_t\$ is selectively measured by a spectrum analyzer (SA) For two-port DUTs, a power combiner is required to simultaneously apply both signals, as illustrated in Figure 7(a) Each SG is equipped with an appropriate filter to reject generated nonlinear signals and prevent intermodulation distortion (IMD).
To enhance return attenuation at the DUT port 1, it may be necessary to incorporate an attenuator (ATT) between the power combiner and the DUT port 1, as the characteristics of the power combiner are typically frequency dependent This is particularly relevant in the three-port configuration illustrated in Figure 7(b).
ATTs are placed between the filter and the Device Under Test (DUT) because passive filters only show a circuit impedance of R0 within the filter's pass band, which does not apply to the frequencies of Intermodulation Distortion (IMD) signals produced by the DUT.
DUT (3-port) Port 1 Port 3 LPF/BPF e b
Figure 7 – Practical setup for the IMD measurement (two-tone test)
The three-tone (triple-beat) test configuration for IMD3 measurement, illustrated in Figure 8, utilizes three signal generators (SGs) to apply sinusoidal signals at frequencies \$f_a\$, \$f_b\$, and \$f_c\$ to the device under test (DUT) The target spectrum component \$P_t\$ at frequency \$f_t = f_c \pm (f_a - f_b)\$ is selectively measured by the spectrum analyzer (SA) Additionally, filters and an attenuator (ATT) are strategically arranged with the power combiner to reject unwanted nonlinear signals and prevent intermodulation distortion (IMD) generation.
SGa and SGb and to improve the return attenuation looking from the DUT port also for frequencies of IMD signals generated in the DUT
Figure 8 – Practical setup for three-tone measurement
Influence of circuit impedance for nonlinearity measurement
This article quantitatively examines the impact of circuit impedance, using the IMD2 measurement of a SAW/BAW antenna duplexer as a case study The duplexer consists of two filters: the transmit (Tx) filter, which connects ports 1 and 2 to transmit signals in the Tx band, and the receive (Rx) filter, which connects ports 2 and 3 to transmit signals in the Rx band.
Ports 1, 2 and 3 are often called the Tx, antenna (ANT) and Rx ports, respectively
Figure 9 – Setup for IMD2 measurement of SAW/BAW antenna duplexers
For the IMD2 measurement, two RF signal generators, designated as “SGa” and “SGb,” are connected to ports 1 and 2, respectively, to simulate the Tx and jammer signals The frequencies \( f_a \) and \( f_b \) of these generators are carefully specified to ensure accurate measurement.
• f a is in the Tx band, and
• f a + f b or f a − f b is in the Rx band This means that
• f b is far from the Tx and Rx bands
The signal "a" from port 1 is transmitted to port 2 via the Tx filter, while the signal "b" from port 2 experiences significant attenuation through the Tx and Rx filters This indicates that the IMD2 signal is primarily produced by SAW/BAW resonators near port 2 and is observed at port 3 after passing through the Rx filter.
Variation of IMD2 output is caused mainly by the following five mechanisms:
• variation of the Tx signal intensity due to impedance mismatching at the Tx port for f = f a ,
• re-entry of the Tx signal to the ANT port due to impedance mismatching at the ANT port for f = f a ,
• variation of the jammer signal intensity due to impedance mismatching at the ANT port for f= f b ,
• re-entry of the nonlinear signal to the ANT port due to impedance mismatching at the ANT port for f = f a +f b or f = f a -f b , and
• variation of detector read due to impedance mismatching at the Rx port for f = f a + f b or f = f a − f b
The fractional error \$\delta\$ of the spectrum analyzer (SA) reading \$b\$ can be approximated by considering the IMD2 signal generated near the device under test (DUT) port 2 This relationship highlights the influence of various factors on the measurement accuracy, emphasizing the importance of precise signal generation in testing scenarios.
The reflectivity for the DUT port-n is denoted as \$S_{nn}\$, while the peripheral circuit's reflectivity from the DUT port-n is represented as \$\Gamma_n\$ Equation (8) highlights the frequency dependence of both \$S_{nn}\$ and \$\Gamma_n\$, as indicated by the added superscript.
Figure 10 shows range of deviation of the SA read resulting from δ in dB, namely the range from 20 log(1-|δ|) to 20 log(1+|δ|) Since | S 32 a ± b | ≈ 1 and | S 21 a | ≈ 1, this result indicates that a
S shall be suppressed better than − 25 dB and − 31 dB to obtain measurement accuracy better than ± 0,5 dB and ± 0,25 dB, respectively
In commercial duplexers, the parameters S 11 a, S 22 a, S 22 a ± b, and S 33 a ± b are approximately zero, while | S 22 b | is around one Therefore, it is crucial to focus on suppressing Γ 2 b, aiming for a suppression level better than -25 dB (or -31 dB) to achieve measurement accuracy within ± 0.5 dB (or ± 0.25 dB).
M ax im um dev ia tion (dB )
Figure 10 – Range of deviation resulting from δ in dB
Influence of circuit nonlinearity
This article quantitatively examines the impact of nonlinear signals produced by peripheral circuits For instance, we analyze the IMD2 measurement of an RF SAW/BAW duplexer, as illustrated in Figure 9 In this scenario, the fractional error \$\delta\$ of the SA read \$b\$ resulting from circuit nonlinearity can be expressed mathematically.
= ± ± (9) where IP2 DUT is the IP2 of the DUT, IP2 n is the IP2 of the peripheral circuit connected to the
The relative phase of the IMD2 signal at the DUT port n is denoted as φ n Given that the conditions | S 31 a ± b S 12 b |