Measuring the Transponder Resonant Frequency and the Q Factor

The precise measurement of the transponderresonant frequency so that deviations from the desired value can be detected is particularly important in the manufacture of inductively coupled transpon-ders. However, since transponders are usually packed in a glass or plastic housing, which renders them inaccessible, the measurement of the resonant frequency can only be realised by means of an inductive coupling.

The measurement circuit for this is shown in Figure 4.47. A coupling coil (conductor loop with several windings) is used to achieve the inductive coupling between transponder and measuring device. The self-resonant frequency of this coupling coil should be significantly higher (by a factor of at least 2) than the self-resonant frequency of the transponder in order to minimise measuring errors.

Aphase and impedance analyser(or anetwork analyser) is now used to measure the impedance Z1of the coupling coil as a function of frequency. IfZ1is represented in the form of a line diagram it has a curved path, as shown in Figure 4.48. As the measuring frequency rises the line diagram passes through various local maxima and minima for the magnitude and phase ofZ1. The sequence of the individual maxima and minima is always the same.

Z₁

M

L₁ i₁

L₂ ?

Figure 4.47 The circuit for the measurement of thetransponder resonant frequencyconsists of a coupling coil L1and a measuring device that can precisely measure the complex impedance ofZ1 over a certain frequency range

0 50 100 150 200

5× 10⁶ 1× 10⁷ 1.5× 10⁷ 2× 10⁷ 2.5× 10⁷

|Z₁| arg(Z₁)

Figure 4.48 The measurement of absolute value and phase at the measuring coil permits no conclusion to be drawn regarding the resonance frequency of the transponder

In the event of mutual inductance with a transponder the impedanceZ1 of the coupling coilL1

is made up of several individual impedances:

Z1=R₁+j ωL₁+Z_T (4.58)

Figure 4.49 shows the locus curve of impedance Z1 measured over a larger frequency range.

The locus curve starts with frequency 0 at originZ1(f)=0. With increasing measuring frequency, the locus curve initially follows a line parallel to the y axis. For low measuring frequencies, the effect of thetransponder oscillating circuitcan still be neglected, soZ1=RL+jωL1.

If the measuring frequency further increases the locus curve becomes a circle to be followed clockwise, which is due to the effect of Z_T in the range of the resonant frequency, i.e. |Z_T|>0.

There a several distinctive points on the circle. These points can also be recognized easily on the line diagram for|Z1|(see Figure 4.48).

At first, there is a point with a maximum valueZ1which can be recognized as a local maximum also in the line diagram. The next distinctive point on the locus curve is the minimum value of phase angleϕ, which can also be clearly recognized in the line diagram (minimum on the dotted line). The phase minimum is followed by a local minimum of valueZ₁after which the locus curve, with increasing measuring frequency, finally ends in a vertical line again. The local minimumZ1

is also clearly visible in the line diagram ofZ1.

The point we are interested in, i.e. the transponder’s resonant frequency, corresponds to the maximum value of the real component of Z1. This point, however, is not visible in the line diagram of|Z1|. In order to determine the resonant frequency of a transponder, we have to measure real componentR of|Z1|with the resonant frequency corresponding to the maximum ofR. An alternative approach would be to measure the value of the transformed transponder impedance by eliminating the influence of the measuring coil (R1, L1)through compensation measurement (short correction; the centre of the circle that the locus curve describes in Figure 4.49 is then situated on the diagram’s re-axis). For this kind of measurement, the maximum value of the transponder impedance corresponds to the resonant frequency.

0

Figure 4.49 The locus curve of impedanceZ1 in the frequency range 1– 30 MHz

Figure 4.50 shows a measurement set-up for measuring the resonant frequency of a contactless smart card. Measuring coilL1and the measuring object, i.e. the contactless smart card on a spacer, are clearly visible on the right hand side of the figure. Figure 4.51 presents a screenshot of the measurement. Correction measurement was used for prior compensation of the measuring coil’s impedance (L1, R1). For the given impedance value, the transponder resonant frequency can be read off as the measuring curve’s maximum at 14.9325 MHz (marker 1).

With this measuring method, it is – under specific circumstances – possible tomeasure the Q fac-tor of the transponder oscillating circuit. TheQfactor measures the voltage and current overshoot in the oscillating circuit at resonant frequency.Bandwidth B of an oscillating circuit is inversely proportional to theQ factor and states a frequency range around the transponder’s resonant fre-quency. At the limits of this range, coupled-in voltage u2 has decreased by 3 dB (factor 0.707) in comparison to resonant frequency. The same applies to currenti2 in coil L2 of the transponder oscillating circuit as it is proportional to voltageu2. As even the measured transponder impedance Z_Tis proportional to voltageu2 or currenti2, respectively, we can determine the 3 dB bandwidth forZ_T und use formula 4.55 to determine theQfactor of the transponder oscillating circuit. Band-widthB then is defined as the frequency range around the transponder resonant frequency at the limits of which the value ofZ_T has decreased by 3 dB (factor 0.707) in comparison to the value measured at resonant frequency.

Figure 4.51 presents an example of a measurement of a transponder’s Qfactor where the Q factor is automatically calculated by the measuring device. The 3 dB bandwidth (BW) is defined

Figure 4.50 Example of a measurement set-up for measuring a transponder’s resonant frequency andQfactor.

To the right, you see measuring coil L1. Above, there is a contactless smart card as the measuring object. Four plastic pins retain it at a predefined distance (reproduced by permission of Infineon Technologies Austria AG)

Figure 4.51 Screenshot of the measurement of a transponder’s resonant frequency andQfactor (reproduced by permission of Infineon Technologies Austria AG)

measurement, we have to compensate for the impedance contributed by the measuring coil (R1, L1) in order to eliminate it from the measurement as it would falsify the result (i.e. without measuring object, the measured value of the impedance should be zero over the entire given frequency range).

Another possible source of error when measuring theQfactor is to set the field strength at a too high value (i.e. the measuring current in coilL1 is too high). This may trigger the shunt regulator or activate the transponder chip which changes the Q factor during the ongoing measurement.

Usually this effect is clearly visible, though, through a distinctive asymmetry or an ‘unsteady’

measuring curve.