**2.5. Characterisation methods**

There are two main methods for characterising filters. The first method is based on time domain analysis, whereas the second is based on frequency measurement. Recently, a pseudo‐time method was introduced to perform tests. The first method is based on time domain reflec‐ tometry/transmission (TDR/T). It involves sending through the filter a short pulse whose duration is selected to reach the frequency of the filter passband. The reflected and/or trans‐ mitted signals are then measured and analysed to obtain the filter behaviour and its time response. Fast Fourier Transform (FFT) could also be used to obtain the frequency response. However, this method requires generating a short pulse and a fast sampling rate. This type of apparatus can be expensive and the obtained measurement does not give better accuracy. This method is seldom used and will not be presented here.

#### *2.5.1. Low power characterisation of S parameters*

Measurement of *S* parameters is performed by using a vector network analyser (VNA). This is one of the best ways to characterise a filter. This measurement method is a component of frequency domain analysis as the VNA sweeps a pure sine signal from a start frequency to a stop frequency, which are defined by the user. It requires an initial calibration step and a second step to de‐embed access lines and/or pads. After all these operations, the component *S* parameters can be analysed and compared with the desired or ideal characteristics. The obtained *S* parameters are composed of numerous frequency measurement points, generally several hundreds, and for each *S* parameter, the module and the phase or the real part and the imaginary part. This method is used both in research laboratories and in industry. In research laboratories, it allows piezoelectric parameters as well as other parameters to be extracted, although it must be linked to a model of the piezoelectric structure or filter. In the industry, the VNA is used, but it is a time‐consuming apparatus because several steps are required before getting the *S* parameters. Furthermore, analysis of *S* parameters must be done to ensure that the devices respond to the desired characteristics. Thus, the cost of the device increases with the analysis time and the type of setup.

### *2.5.2. High power characterisation*

with *Z*<sup>m</sup> =*ρ*m*V*m being the acoustic impedance of each layer, *V*m the longitudinal wave velocity, *t*<sup>m</sup> the thickness and *ρ*<sup>m</sup> the density. Mechanical losses are considered in each material in the expression of *V*m, which is proportional to the complex elastic constant of the considered material. The surface *S*m involved in the model is equal to the active surface of the piezoelectric

The last interesting feature of electrical models is that they can be implemented in electric and RF simulators, such as ADS from Keysight. It allows for use of all possible simulations available in this class of simulators, such as *S* parameters, which allow electromagnetic wave propaga‐ tion and electrical impedance matching with input and output ports of the filter to be taken

There are two main methods for characterising filters. The first method is based on time domain analysis, whereas the second is based on frequency measurement. Recently, a pseudo‐time method was introduced to perform tests. The first method is based on time domain reflec‐ tometry/transmission (TDR/T). It involves sending through the filter a short pulse whose duration is selected to reach the frequency of the filter passband. The reflected and/or trans‐ mitted signals are then measured and analysed to obtain the filter behaviour and its time response. Fast Fourier Transform (FFT) could also be used to obtain the frequency response. However, this method requires generating a short pulse and a fast sampling rate. This type of apparatus can be expensive and the obtained measurement does not give better accuracy. This

Measurement of *S* parameters is performed by using a vector network analyser (VNA). This is one of the best ways to characterise a filter. This measurement method is a component of frequency domain analysis as the VNA sweeps a pure sine signal from a start frequency to a stop frequency, which are defined by the user. It requires an initial calibration step and a second step to de‐embed access lines and/or pads. After all these operations, the component *S* parameters can be analysed and compared with the desired or ideal characteristics. The obtained *S* parameters are composed of numerous frequency measurement points, generally several hundreds, and for each *S* parameter, the module and the phase or the real part and the imaginary part. This method is used both in research laboratories and in industry. In research laboratories, it allows piezoelectric parameters as well as other parameters to be extracted, although it must be linked to a model of the piezoelectric structure or filter. In the industry, the VNA is used, but it is a time‐consuming apparatus because several steps are required before getting the *S* parameters. Furthermore, analysis of *S* parameters must be done to ensure that the devices respond to the desired characteristics. Thus, the cost of the device increases with

into account, harmonic balance simulation or transient simulation.

method is seldom used and will not be presented here.

*2.5.1. Low power characterisation of S parameters*

the analysis time and the type of setup.

plate *S*p.

216 Piezoelectric Materials

**2.5. Characterisation methods**

piezoelectric materials used to realise filters can be submitted to high RF power compared with their micrometric dimensions in compact structures [18]. For example, the maximum power emitted by most mobile phones can reach 2 W or 33 dBm. Submitted to this high power, the first resonator of a filter will exhibit a nonlinear behaviour. It is important first to characterise the filter with this high power and next to extract the nonlinear changes of the material constants, such as the piezoelectric constant, the permittivity or the elastic constant.

Two types of measurement can be done. The first is the third‐order intercept point (*IP*3) measurement, and the second is the 1 dB compression point. For the *IP*3 measurement, two sine tones of closed frequencies are combined and applied at the input of the filter. When nonlinear behaviour becomes important, the two frequencies will create an intermodulation and thus an unwanted spurious frequency only due to high power. A measurement configu‐ ration type is shown in **Figure 18**.

**Figure 18.** Experimental setup for intercept point measurement.

**Figure 19.** *IP*3 measurement.

Signals coming from generators are combined, amplified and applied at the input of the filter. At the output of the filter, a spectrum analyser is used to measure the amplitude of each frequency generated by the generators and the frequencies coming from the intermodulation. Then the output power is represented as the function of the input power for the fundamental frequency and for the third harmonic. The point at the intersection of both lines gives the *IP*<sup>3</sup> point. An example is given in **Figure 19**.

A VNA must be used to measure the compression point at 1 dB. The principle is to measure the transmission coefficient (*S*21) as the function of the input power at a fixed frequency, in general the central frequency of the filter passband. A sample measurement setup is given in **Figure 20**. Port 1 is dedicated for excitation, whereas port 2 measures the output signal of the filter. With a directional coupler, the input power of the filter can be obtained and is measured by the reference port of the VNA. A special configuration of the VNA allows for the results shown in **Figure 21** to be obtained directly, where *P*1 is the 1 dB compression point. *P*1 allows the input power to be determined when the output level decreases by 1 dB as compared with small input power. In most cases, this input power is considered to be the maximum allowable power before reaching the nonlinear behaviour.

**Figure 20.** Experimental setup for 1 dB compression point measurement.

**Figure 21.** Insertion loss measurement at a fixed frequency and 1 dB compression measurement.

High power measurements can be used to acquire the behaviour of the filter, but also associ‐ ated with a model, it is possible to extract the variations of the main parameters in the function of power. This was performed for AlN by Sahyoun et al. [27].

#### *2.5.3. Test of filter*

Signals coming from generators are combined, amplified and applied at the input of the filter. At the output of the filter, a spectrum analyser is used to measure the amplitude of each frequency generated by the generators and the frequencies coming from the intermodulation. Then the output power is represented as the function of the input power for the fundamental frequency and for the third harmonic. The point at the intersection of both lines gives the *IP*<sup>3</sup>

A VNA must be used to measure the compression point at 1 dB. The principle is to measure the transmission coefficient (*S*21) as the function of the input power at a fixed frequency, in general the central frequency of the filter passband. A sample measurement setup is given in **Figure 20**. Port 1 is dedicated for excitation, whereas port 2 measures the output signal of the filter. With a directional coupler, the input power of the filter can be obtained and is measured by the reference port of the VNA. A special configuration of the VNA allows for the results shown in **Figure 21** to be obtained directly, where *P*1 is the 1 dB compression point. *P*1 allows the input power to be determined when the output level decreases by 1 dB as compared with small input power. In most cases, this input power is considered to be the maximum allowable

point. An example is given in **Figure 19**.

218 Piezoelectric Materials

power before reaching the nonlinear behaviour.

**Figure 20.** Experimental setup for 1 dB compression point measurement.

**Figure 21.** Insertion loss measurement at a fixed frequency and 1 dB compression measurement.

The characterisation of filters using a VNA is a good way to obtain much information about the behaviour of structures. Nevertheless, when devices must be tested after fabrication, this kind of measurement is time‐consuming and requires the calibration of the VNA after the exploitation of the measured data. An interesting alternative is to perform a test in order to verify if the filter can be used or not with only one measurement and with a more simple measurement setup. Another requirement can be to determine the behaviour in conditions close to the real conditions of operation. For this purpose, a digitally modulated signal can be used. The carrier frequency can be tuned in the passband of the filter, and a QPSK modulated signal is the best trade‐off to perform the test. It is possible by analysing the output signal to see if the filter responds to a minimum requirement in terms of insertion losses and passband. This technique presented by Sahyoun et al. [28] offers the possibility to discriminate filters.
