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September 25, 2016

## Capacitors

Here is an introduction to various types of capacitors used at microwave frequencies. This is a companion page to our pages on microwave inductors and microwave resistors.

Here's a clickable index to our material on capacitors:

Capacitor background and definitions

Capacitor materials (separate page)

Microwave capacitor model

Capacitor mathematics (separate page)

Capacitive reactance

Parallel-plate capacitance

Sheet capacitance

Capacitor resonances

Charge storage calculation (separate page, new for March 2007!)

Single-layer capacitors

Multi-layer ceramic capacitors

Separate page on this topic, new for September 2008

Electrolytic capacitors

ESR effects (separate page, new for September 2008)

### Capacitor background and definitions

Microwave capacitors are used as tuning elements, or as components in simple or complex filter structures. Used as a tuning element, a high tolerance is often required on a low capacitance value. Used as a DC block or bypass, usually all that you will care about is a that your RF signal sees a low impedance.

The unit of capacitance is the Farad, named after Michael Faraday. At "classic" microwave frequencies, such as X-band, capacitance units of picofarads (10-12 Farads) are commonly used. Many RFIC-type people use nanofarads (10-9 Farads) just as often, and in millimeterwave applications (i.e. where "real men" work), we use femtofarads (10-15 Farads) sometimes (thanks for the correction, David!)

A capacitor often does not act as a capacitor at microwave frequencies. Microwave capacitors must be small enough to be considered lumped elements. Axial-leaded capacitors are not useful at microwave frequencies because of the need to keep small dimensions.

#### DC blocks and RF bypass capacitors

Both of these are simple filters employing microwave capacitors. A DC block is a series capacitor that has low reactance for the RF frequency of interest (an RF short), but blocks DC because it is an open circuit at zero Hertz. An RF bypass is shunt (parallel) element that acts like a short circuit to microwave signals, but here it is meant to reflect RF signals by shorting them out.

#### Charge-storage capacitors

These are used to hold up the voltage during pulsed operation. They are not usually microwave-style capacitors, and are most often electrolytics.

### Microwave capacitor model

Below is the classic lumped-element model of a capacitor for microwave circuits. Physical models of capacitors are also used at microwave frequencies, especially in MMIC modeling, we'll get into that topic another time.

The element denoted "C" in the model is the nominal capacitance value, the rest of the elements are considered parasitics. LS is the self-inductance of the structure. The equivalent series resistance (ESR) is the real part of the series impedance of a capacitor, and is what causes loss due to heat. The parallel capacitance CP also causes some trouble, but can often be ignored because we try to operate below the frequency where this causes a resonance.

The capacitor quality factor (Q) equation can be found on our capacitor math page.

### Multi-layer ceramic capacitors

This topic now has its own page.

Multi-layer ceramic capacitors are used as surface mount devices in microwave printed wiring boards, and sometimes in hybrid integrated circuits DC filtering. Multilayer technology allows high capacitance in small volume. Sizes of multilayer capacitors that are popular for microwave work are 0402, 0603 and 0805. These sizes are "decoded" by noting that the number"02" means 0.02 inches, "04" means 0.04 inches, etc. The Metric system bows down to the English system again!!!

For surface-mount caps such as multilayer ceramic and tantalum, the coefficient of expansion becomes important when you operate large size caps over a wide temperature range.

Two internet legends about multi-layer caps, which we will wait for our audience to support or refute...

You can increase the SRF by mounting a multilayer with the "fat" dimension up. (OK, this needs a figure...)

You can screen multi-layer caps for low ESR by zapping them in a microwave, and throwing out the ones that heat up the most.

### Single layer capacitors, aka thin-film caps (TFCs)

Single-layer caps are the choice for the highest frequency response. Also called thin-film capacitors, when realized monolithically, they can be used as in microwave circuits well beyond W-band (<110 GHz). TFCs are used in MMICs and RFICs for bypass,DC blocking and RF tuning elements. A good process can provide +/-10% accuracy, it all comes down to how well you can control the dielectric thickness. The usual dielectrics are silicon nitride and silicon oxide. For capacitors on MMICs, the upper limit is on the order of 20 pF.

The TFC is formed by metalizing a substrate, coating it with a thin dielectric, then adding a top metal to form a sandwich. They are sometimes referred to as MIM (metal-insulator-metal) caps.

If anyone offers to make TFCs on an alumina substrate, be aware that this is no easy task. The grain structure of polished alumina is very rough compared to typical dielectric thickness (a few thousand Angstroms) and short circuits are the defect of choice here.

### Metal oxide semiconductor (MOS) capacitors

These capacitors came as a by-product of the silicon revolution. Silicon circuits are isolated by growing silicon oxide. Add a layer of metal on top (almost always aluminum in a silicon process) and you can create a capacitor. This type of capacitor provides excellent microwave response for values up to hundreds of pF.

MOS caps are different from MIM caps in that the base "metal" in MOS is a semiconductor (silicon), which provides electrical contact through the backside. The backside of a MOS cap could be plated with aluminum or left bare. Other variations on this theme include MNS (metal nitride silicon).

### Single-layer ceramic caps

Single-layer ceramic caps are formed by metalizing a thin ceramic substrate and dicing it. Often the ceramic has very high dielectric constant so that small capacitors (less than 1mm on each side) can provide 100 pF or more. High DK often comes at the price of poor temperature stability.

### Electrolytic capacitors

Electrolytic capacitors provide the highest density of capacitance, with values into tens of micro-Farads. Often they are made of tantalum. These are not actually microwave-quality, but are often used as power supply filtering for microwave circuits. Linear regulators always need at least two electrolytic caps, one on the input and one on the output, to remain stable. In pulsed applications, electrolytics are configured in banks to provide charge storage such that the voltage droop is controlled. Learn about charge storage here and equivalent series resistance here. What's the difference between droop and drop? Lean that here.

Electrolytic caps are polarized, meaning that you have to be careful which way you hook up DC voltages across them. Bias them backwards and they could set off the smoke detector!

How tantalum capacitors are made is an interesting process. Tantalum is processed into very tiny spheres, which are compressed and sintered together into a sponge-like structure with mucho surface area per unit volume (the smaller and more uniform the sphere size, the more area). Tantalum pentoxide is grown onto this medium, which acts as the dielectric layer. The structure is infiltrated with another conductor, contacts are added, and voila, you have a high-density capacitor!

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