# Parasitics & Capacitor Selection, Part 5: Q

In part 4A of this series, which examined dissipation factor (DF), I mentioned that the Q of a capacitor is the reciprocal of its DF. So, like DF, Q is a dimensionless number. It represents the ratio of the maximum energy stored to the power loss in a system at a given angular frequency rather than the inverse (DF). Unlike DF or direct current leakage (DCL), though, Q was not originally an abbreviation for anything. However, its origin as a figure of merit for the sharpness of an inductor's self-resonance has led to its being commonly called “quality factor,” especially in RF applications that require a high Q number (which is not to be confused with the Q that represents the charge on a capacitor in electrostatics).

What does Q represent, and how it has become a useful metric in high-frequency applications? It was originally a measure for inductors at self-resonant frequency (i.e., the frequency at which a signal experiences the minimum inductive reactance, which, at that point, is equal to the equivalent series resistance of the device). Inductors behave inductively at frequencies below self-resonance and capacitively at frequencies above self-resonance. Inversely, capacitors behave capacitively at frequencies below self-resonance and inductively at frequencies above self-resonance. At their self-resonant frequencies, both inductors and capacitors act as pure resistors, with no additional contribution from inductive or capacitive reactance.

In the capacitor industry, a part with very low DF (and hence high Q) will have a “sharp” self-resonant characteristic. If an AC signal with a certain current level over a wide frequency range is passed through such a capacitor, the portion of the signal that corresponds to the capacitor's self-resonant frequency will pass through with minimum resistance. The sharpness of a capacitor (how selective it is) is measured in terms of the bandwidth that is passed through. For a capacitor with a symmetrical characteristic, the bandwidth is defined as the frequency spread at which the signal is above half the maximum power. Since power is proportional to the square of the current, this is equivalent to 0.707x the maximum signal current (1/√2 = 0.707), which can also be expressed on a logarithmic scale as -3dB. So Q is a useful metric in that it can be used to calculate a capacitor's bandwidth easily and accurately (i.e., the capacitor's self-resonant frequency divided by Q).

Figure 1

This graph illustrates the bandwidth (or range of frequencies) over which a capacitor will operate with low power loss (defined as -3dB or about 71% of peak power). The higher a device's Q, the narrower the bandwidth. For a 1pF 0402 capacitor at 1 GHz, the bandwidth is 1.38 MHz.

One of the most common applications for a high-Q capacitor is a notch filter. This device, which allows only a narrow range of frequencies to pass, is often employed in a broad range of RF applications to filter a signal at a specific frequency ranging from GSM (in the 950MHz range) to WiFi (in the 5GHz range).

Figure 2

The losses through the capacitor will increase (and its Q will drop) as is it operated at higher frequencies approaching its self-resonant frequency (SRF). This graph shows how Q varies with frequency for different capacitance values. Since it is not on a logarithmic scale, Q will decrease dramatically as frequency increases. For reference, this chart also shows the SRFs for a number of these capacitance ratings.

Typically, low-capacitance (pF range) multilayer ceramic capacitors (MLCCs) using low-loss dielectrics (such as NP0) are designed into high-Q applications, since they have self-resonance in the GHz range, and their ordered construction (evenly spaced electrode layers with little geometric variation) makes for a sharp self-resonant frequency. Additionally, advances in MLCC size reduction have made it possible to design 01005 size NP0 MLCCs with both copper electrodes for good signal current handling and a Q of ~290 at 1 GHz for a 4pF capacitance value, which translates into a bandwidth of 3.4 MHz at 1 GHz.

However, thin-film technology, the primary alternative to high-Q MLCCs, can enable even higher-Q capacitors. Thin-film capacitors using very low-loss, ultra-stable SiO2 dielectrics in an 0402 size with a 0.1pF rating have a typical Q of 850 at 1 GHz, which translates to an even tighter bandwidth of 1.2 MHz at 1 GHz. Further, thin film's narrow bandwidth capability enables high Q repeatability for a given rating from part to part and from lot to lot.

Also, though MLCC construction exhibits regular geometry, a few minor variations can occur during production, including variations in the initial dielectric laydown, electrode plate overlap due to the screen printing process, and shrinkage due to temperature differential across the oven during firing. By contrast, thin-film dielectric is manufactured using a precise vapor deposition process, and the construction process for thin-film capacitors does not require an equivalent to the high-temperature firing process used to create MLCCs. Moreover, the resultant capacitors feature a single dielectric layer and a single pair of high-registration photo-lith electrodes, eliminating higher-frequency harmonics that can arise in the multilayer design.

An emerging technology, multilayer organic capacitors (MLOCs), is offering design engineers a promising alternative to the MLCCs and thin-film capacitors most frequently deployed in high-Q applications. MLOCs are polymer-based capacitors, fabricated using laser direct imaging, that use high-conductivity copper interconnects in a multilayer fashion, allow for tight tolerance control. The devices feature an inherently low profile and provide state-of-the-art low equivalent series resistance (ESR) and high self-resonant frequency performance in RF applications that demand high Q and can support frequencies well above 1 GHz. For example, a 0603 size MLOC with a 0.1pF rating will have a typical Q of 1,100 at 1 GHz.

Both MLO and thin-film technologies can go beyond simple capacitor constructions and integrate equally high-Q inductor elements to enable the production of many other useful RF devices, such as 3dB couplers, band pass filters, low pass filters, diplexers, and crossovers.

What do you do if you don't want high Q — if, instead of a sharp resonant point, you need, say, a very broad resonance with a flat characteristic? This is best achieved with technologies that have little regularity in the dielectric geometry, such as tantalum capacitors, which are made by sintering together nano-sized particles of tantalum metal powder to create a structure similar to a microscopic sponge. Despite being formed over the whole microscopic area with precision uniformity at the angstrom level, the tantalum dielectric is geometrically convoluted and has a completely different frequency response to the tuned geometric structure of MLCCs. This results in a very flat frequency response, which, unfortunately, rolls off at relatively low frequencies (1–100 MHz).

The challenge for high-frequency applications lies in designing a broadband capacitor capable of operating “from DC to daylight.” This is an important consideration for effective DC blocking, where the capacitor can be used to eliminate the DC bias from an input while effectively transmitting all signal frequencies. Recent technological advancements have enabled the manufacture of a longstanding item on designers' wish lists: an ultra-broadband capacitor that specifically addresses DC blocking issues from 160 KHz (at -3dB rolloff) to 40 GHz.

This part, made with precision thin-film termination processes, is designed to be completely orientation insensitive and is available in standard EIA sizes from 0201 to 0603. Also, since the frequency range makes this capacitor ideal for use in optical subassemblies, it is available with gold termination suitable for wire-bonding processes.

## 2 comments on “Parasitics & Capacitor Selection, Part 5: Q”

1. RedDerek
September 2, 2014

Chris, thanks for the insight of capacitors and what is on the horizon.

2. Chris-R
September 5, 2014

You're welcome – and feel free to contact me if you have any specific component questions

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