Multilayer ceramic capacitors (MLCC) are widely used in today's electronic products due to their low cost, high volumetric efficiency and low equivalent series resistance. These advantages make the MLCC nearly perfect for a variety of applications, such as output capacitors for power supplies and local decoupling capacitors for integrated circuits. The different types of MLCC are mainly defined by their temperature coefficient, which is the amount of change in capacitance over a specified temperature range. According to NP0 or C0G, the change of capacitance of Class I MLCC in the operating temperature range must be less than +/–30ppm, while the variation range of Class II MLCC can be between +/–15% (X7R) to +22%/ Between –82% (Z5V)[1].
The temperature coefficient of the MLCC is directly affected by the ceramic material that forms the capacitor dielectric. In addition, the dielectric material can also determine the electrical characteristics of the capacitor. Class II dielectrics (X7R, Z5U, Z5V) are often referred to as "high-k" ceramics because of their relatively high relative dielectric constants between 3000 (X7R) and 18000 (Z5U). Class I C0G capacitors have a relative dielectric constant ranging from 6 to 200 [1]. Dielectric materials have a higher relative dielectric constant, which means that the capacitance of high-k MLCC is much larger and the package size is smaller than the COG type.
However, there are also shortcomings in enjoying these advantages. For example, a high K MLCC will exhibit a significant voltage coefficient, meaning that the change in capacitance depends on the applied voltage. In AC applications, this phenomenon can manifest as waveform distortion and can degrade overall system performance. When printed circuit board (PCB) area and cost become the primary design constraints, board and system level designers may consider using high K MLCCs in the circuit to cause significant signal distortion in the signal path.
Demonstrate high K MLCC distortion
Circuit examples such as active filter circuits, anti-aliasing filters for data converters, and feedback capacitors in amplifiers can cause distortion when using high K MLCC. To illustrate this effect, we designed a 1kHz Butterworth active low-pass filter using the Sallen-Key topology using TI FilterPro software. For very common applications such as active filters, the distortion caused by the capacitor can degrade overall circuit performance. Many designers use low-resistance values ​​to reduce the output noise generated by the resistors, which also increases the capacitance required for a particular corner frequency. For this design decision, the high-k MLCC is probably the only capacitor on the market that meets capacitance, board area, and cost requirements.
The filter circuit shown in Figure 1 identifies the passive component values, replacing capacitors C1 and C2 with MLCCs with different dielectric types and package sizes, allowing direct comparison of measured values ​​between different types of capacitors. . All capacitors used in the test are rated at 50V.
Figure 1: Sallen-Key low-pass filter with a corner frequency of 1kHz
For example, we chose the high performance audio op amp OPA1611 as the low noise and low distortion base of the circuit. To minimize distortion outside the capacitors, all resistors are available in high precision thin film resistors in the 1206 package. According to "Design of Active Frequency Division Amplifiers", some resistors can produce distortion similar to that formed by capacitors [2]. Finally, the +/–18V supply is used to power the circuit to prevent the amplifier from affecting the measurement due to saturation.
Total Harmonic Distortion and Noise (THD+N) is an indicator parameter used to quantify anomalous content caused by circuit noise and nonlinearities in the signal. This quantization factor can be expressed as the ratio between the harmonics and the system RMS noise voltage and the RMS fundamental voltage [3]. Harmonics or signals at integer multiples of the input signal result from nonlinear behavior of passive components and integrated circuits. The total noise of the circuit is caused by the noise inherent in the integrated circuit and the thermal noise of the resistor, and may also be externally coupled into the circuit. Equation 1 is THD+N as the calculation of the amplitude ratio, where VF is the RMS fundamental voltage, VN is the RMS noise voltage, and VI is the RMS voltage of each harmonic.
The THD+N measurement is done in the filter circuit using a 1Vrms signal with a frequency range of 20Hz to 20kHz and a measurement bandwidth of 500kHz. Figure 2 shows the THD+N performance (dB) of a circuit measured with respect to 1Vrms for different types of capacitors. Excellent performance is achieved with the C0G dielectric MLCC in the 1206 package: THD+N measured in the filter passband is at the noise floor of the measurement system. In addition, C0G capacitors in the 0805 package were also tested and showed identical performance levels, which are not listed in this figure for simplicity. Since the attenuation of the filter reduces the ratio of the signal amplitude to the noise floor, THD+N is expected to increase above the filter corner frequency.
If we replace the capacitor with the X7R in the 1206 package, we will observe that the circuit performance will immediately decrease. The THD+N frequency is 20dB with a minimum increase of 15dB and measures a maximum THD+N increase of 35dB between 400 and 800Hz. Switching to an X7R capacitor in a smaller 0603 package further increases THD+N by 10dB over a significant spectrum. Since the op amps and resistors of the filters in all tests have not changed, the increase in the THD+N value must be due to the extra harmonics generated by the X7R capacitor in the circuit output signal.
Figure 2: THD+N measurement results for the Sallen-Key low-pass filter
Figure 3 shows the 500 Hz sine wave spectrum obtained at the filter output when using 0603 and 1206 X7R capacitors. The spectrum contains a large number of fundamental waves and is dominated by odd-order harmonics. However, when a circuit is built using a 0603 X7R capacitor, harmonics above 20 kHz are unexpectedly observed with a 500 Hz input signal.
Figure 3: 500Hz sine wave spectrum obtained at the output of the low-pass filter circuit
How to identify the source of distortion
When engineers face the need to trace high-level distortion, it may not be possible to immediately determine if there is a problem with an integrated circuit or a passive component. One way to determine the primary source of distortion is to measure the THD+N of the circuit over a very wide range of signal levels (Figure 4). In Figure 1, the THD+N value of the Sallen-Key filter is obtained with a 500Hz fundamental at a signal level between 1mVrms and 10Vrms. When a circuit is built using a C0G capacitor, THD+N is reduced as the signal level increases, eventually reaching the noise floor of the measurement system at a signal level of 2Vrms.
Figure 4: Filter circuit THD+N for increasing the signal level (500 Hz fundamental)
The downward sloping curve indicates that the circuit noise generated by the op amp and resistor is a major factor in the THD+N calculation. In this example, the measured THD+N will decrease as the signal level increases because the ratio of the signal voltage to the noise voltage is increased. Conversely, the nonlinearity of passive components is exacerbated at higher signal levels and increases the distortion tendency as the signal level increases [2]. This can be confirmed by replacing the capacitance in the filter circuit with an X7R capacitor. The X7R capacitor in the 0603 package begins to increase in distortion as the signal amplitude reaches 20mVrms. X7R capacitors in the 1206 package exhibit similar behavior, but the increase in distortion trend begins at 40mVrms. Therefore, if the circuit tends to increase in distortion as the signal level increases, passive components (resistors or capacitors) are likely to be the dominant limiting factor in circuit performance.
Since the distortion of the passive components increases correspondingly with the increase of the signal level, the distortion of the filter circuit reaches a maximum when the maximum voltage is applied by the capacitor [2]. A graph of the voltage and frequency of the circuit components can be plotted using the AC transfer characteristics analysis function in TI's free SPICE simulator Tina-TITM. Figure 5 shows the combined voltage of capacitors C1 and C2 over the frequency range of 20 Hz to 20 kHz and the variation of filter THD+N with X7R capacitors (1206 package). The voltages of the capacitors C1 and C2 are summed by the root square summation method, and the maximum value appears near 600 Hz. Figure 5 shows that there is a close relationship between the maximum value of the capacitor voltage and the maximum distortion point, and it is well illustrated that the capacitor is the source of additional distortion produced by the filter output. If the total amount of distortion produced by the two capacitors is not the same, then there will be some unequal between the two measurements. In addition, further analysis can be performed by determining the signal gain of each capacitor [2].
Figure 5: Combined capacitor voltage and measured THD+N results for the low-pass filter circuit
in conclusion
The performance of analog circuits is largely influenced by the type of capacitor used during construction, and active filters can be used to clarify this principle. When a circuit is built using a C0G capacitor, the performance of the circuit is high. However, once the capacitor is replaced with the X7R dielectric type, the performance of the circuit is significantly reduced. X7R capacitors introduce a large number of harmonics into the signal path, with odd harmonics being the dominant factor in producing THD+N. In particular, X7R capacitors in the 0603 package show the worst performance, while the X6R capacitors in the 1206 package achieve very little performance gain.
Both of these techniques help engineers determine the source of distortion in the circuit. First, measuring THD+N over a wide range of signal levels is a very practical way to determine if circuit performance is limited by the linearity of integrated circuits or passive components. The distortion caused by the nonlinearity of passive components tends to increase as the signal level increases. Second, TINA-TI can correlate the frequency at which the maximum distortion occurs with the frequency at which the component applies the maximum voltage to determine which passive components are the source of the distortion. Although the advantages of high-k MLCCs are helpful for engineers in many applications, it is not advisable to use high-k MLCCs if the capacitor voltage drop in the signal path of the system is significant and causes distortion.
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