**Introduction - **
Capacitors have always been used to provide a path to ground for high frequency signals on a conductor,
while allowing DC or other low
frequency signals to pass along the conductor freely. This is referred to as a "bypass" capacitor. Closely related are capacitors used for power
filtering applications where they are often combined with series inductors or resistors. Traditionally, wideband bypass capacitors
involved electrolytic or tantalum capacitors that suffered from excessive series inductance and resistance at high frequencies.
Attempts to solve this issue by paralleling smaller capacitors have been shown to be fundamentally detrimental [note 1].
However, in recent years the
manufacturing technology for multilayer ceramic capacitors (MLCC) has produced
very high capacity values in small surface-mounted packages [note 3]. These MLCC components
offer ways to improve the effectiveness of bypassing by using multiple capacitors all of the same value.
While improving circuit performance, this also makes circuits simpler and less costly. This note explores a few fundamental ways to do this.

**What not to do -** The section of the Experimental Methods book, referenced in note 1,
covers the problems associated with building wideband bypass capacitors by paralleling different values. Unless
the application is unusual and the implications of paralleling different values has been well studied, the best rule is
"to not do it!" A measured example, illustrating the problems is shown in Figure 1.

The impedance plot, Figure 1, is an example of undesired consequences of parallel capacitors. The several peaks in impedance are the result of the inductance associated with a large value capacitor parallel resonating with a smaller capacity. For example, the parallel resonance at about 260 MHz raises the impedance to around 13 Ohms, making the bypass of little effect. In all cases, the parallel and series resonances will alternate as the frequency goes up. In some cases, losses within a capacitor may make the resonance less obvious, but they are present. The next section deals with using multiple identical capacitors to avoid these problems.

Another, not wrong, but out-of-date method of bypassing is to have one or two 470 pF or 0.001uF disc caps placed across the line to be bypassed. This approach became popular in the 1950's when TVI was a big problem. The disc capacitors were 0.25 inches in diameter and had enough lead inductance to have series resonance roughly in the VHF TV spectrum. I dug in the junk box and came up with a pair of 470 pF disc caps and mounted these with short leads (about a tenth inch, each) to a test fixture.

The measured data shows this system to be quite successful at the VHF TV band, around 54 to 216 MHz, where the impedance is below 2-Ohms. The 6 nH of each cap is series resonated with the 470 pF at about 100 MHz. The 2 to 30 MHz impedance is not so good, but for tube equipment, it was probably adequate. On the high side, the impedance was acceptable in the hundreds of MHz. Note that since these two capacitors are identical, the series resonant frequency is the same as would be seen for a single capacitor. For the general applications of these disks caps, the series resonance is a feature. So, they did what was needed, but, as will be shown, with today's miniature devices we can do much better.

**Identical Values of Capacity - ** The MLCC capacitors offer two major advantages. Their small size reduces the effective
series inductance that limits high frequency performance, while the combination of high dielectric constant
insulation and exceedingly close plate spacing produces a
high capacity. For these experiments I chose to use an 0805 size chip with a capacity of 0.47 uF. This type is readily available in minimum
breakdown voltages of 50 and cost only a few US pennies. The particular capacitor tested in this first example is a Samsung CL21F474ZBFNNNG sold
by DigiKey as 1276-6499-1-ND. This has a Y5V dielectric characteristic which has a poor temperature characteristic of +22% –82% over
a -30 to +85C range, but a compensating feature of very high dielectric constant.

This note looks at shunt capacitors in identical pairs. Relative to a single cap, this doubles the low frequency capacity, cuts the high frequency series inductance in half, but does not cost much money or board space. Clusters of 4 such caps at 45 degree angles are practical as well. Beyond that point, the layout gets crowded and going to multiple stages of filtering may be best. No matter how many capacitors are paralleled, they should, as much as possible, come to a single point on the conductor being bypassed. For instance, do not place the capacitors along the conductor on one side, but rather, for a pair, place a capacitor on each side, coming together on the conductor.

Figure 3 shows the measured magnitude of the impedance for the two 0.47 uF capacitors in parallel. The most obvious feature is the deep null at 5.0 MHz. This is the series resonance of each capacitor along with the series inductance of the small package. Roughly speaking, this puts the inductance at 2 nH. This is in good agreement with the inductance found from the reactance measurements made well above the series resonance. It should be noted that these measurements were made with the chips soldered directly to a UG-1094 BNC connector with the teflon and center pin cut back to the barrel (Figure 4). Use of these capacitors on a PC board would require ground vias that could increase the effective series inductance some.

A very easy method to roughly characterize the chip capacitors is to find the low frequency capacity from the straight line region on the left side of the plot, the series inductance from the right side straight line and the series resistance from impedance the bottom of the null. The least accurate of these three numbers is probably the resistance, which is very difficult to measure with a 50-Ohm system. Better accuracy comes from insertion-loss measurements made with two chips shunted across a 50-Ohm transmission line. In the case of the two 0.47 uF chip caps, the insertion loss is 73.6 dB corresponding to a series resistance, for each capacitor, of 0.011 Ohms. This null is of course at about 5 MHz. So now the simple series RLC model is 0.45uF, 2 nH and 0.011 Ohms.

More detailed models of the MLCC components are not generally needed. But the measured data showed a decrease in capacity from audio frequencies through the 100 KHz range, as is known for the high dielectric constant insulating materials. Additionally, the effective inductance above the hundreds of MHz decreases a small amount with increasing frequency. As was pointed out by IN3OTD this behavior is again expected [see note 7].

One to four of these 0.47 uF components can make a very effective RF bypass for the 0.5 to 500 MHz region, and with a bit of care can be applied at a wider frequency range.

**Going to lower frequencies - ** Suppose that you need more effective bypassing at frequencies below 0.5 MHz, or so.
The obvious solution is to use larger values of capacity. One concern is that this large C will increase the series inductance and thus reduce
the performance at high RF frequencies. This is not the case, and in fact the opposite is true. Measurements were made on a single
1210 chip 100 uF. Figure 4 shows the result for two in parallel, created by halving the measured impedance for a single C.
The graph shows that the
impedance stays below 1-Ohm all the way from 1 kHz to 400 MHz. The noisy looking data around 1 MHz is exactly that.
The impedance is difficult to measure, again. The insertion loss measurement put the series resistance at 0.0016 Ohms.
At this point the simple series RLC model is 90uF, 0.9 nH and 0.0016 Ohms.
This is outstanding broadband performance.

As of this 2017 writing, the factors keeping the 100 uF category of MLCC's from being a complete solution are voltage ratings and cost. Looking at Mouser and DigiKey, the highest voltage seems to be 16 Volts and the cost is in the US $2 range for small quantities down to about $1 in 100's. Additionally, if the frequency range of use is into microwave frequencies, one needs to be cautious of the effects of series inductance.

**Performance of filters - ** Many bypass applications are trying to prevent interaction between a circuit, such as
an amplifier, and the outside environment, such as a power supply. There are endless variation on this situation
but they all come under the general category of filtering. Here we will just take a sample of a few filter circuits to get
an idea of the performance of multiple MLCC components.

First, lets look at low power filter built from a parallel pair of our 0.47 uF chips and two ferrite beads, in series on each end, forming a 'T' circuit. Sticking to the 0805 package for the beads (historically, they were actual beads around wires, so we retain the term), one possibility is a Murata product, BLM21PG331SH1D. This is referred to as a 330-Ohm bead which is the rough impedance somewhere in the 200 MHz range. Murata rates this component for up to 1.5 Amps of current, so it is suitable for many circuits. Other 0805 beads are available with less inductance but higher current ratings.

We were able to think about the capacitors in simple terms of either an C, R or L, depending on the frequency. This is not the case for the ferrite bead. The graphs of Figure 5 shows the series resistance and reactance through the full frequency range. In general, the two components of impedance are commensurate in values and need to be considered together. This represents a lossy characteristic that tends to prevent big resonant peaks or dips, making for a wideband series element for our filter. It also suggests that both components of impedance be plotted separately, and thus the added graph.

Constructing the 'T' filter on a small piece of 0.063-inch thick PC board with coaxial connectors makes insertion loss measurements practical. Figure 6 is a plot of the resulting insertion loss. This is measured between a 50-Ohm generator and a 50-Ohm load. There is no particular reason to feel that this is the right choice of measuring impedance levels, but was used because it is common for commercial filters, and it is consistent with available network analysers. In addition, it is as reasonable a value as any other.

This is looking useful. At least 60 dB of insertion loss is achieved from 2.8 to 600 MHz, covering a large number of amateur bands. The amount of board space required is small and the part cost, even quantities like 10 is about 30 cents.

The next obvious step is to change the capacitors to the 100 uF type, keeping the beads. Figure 7 shows the resulting insertion loss.

Using the 100 uF capacitors produces an insertion loss of over 40 dB from 4 kHz to 2 GHz. The 60 dB range is from 45 kHz to 750 MHz. This sort of filtering performance allows excellent isolation of circuits, even when they are all built on the same PC board. It also is an excellent basis for taking DC and low frequency signals on and off of boards.

**Measurement Methods -**
The frequency range being used here ranges from 10 Hz to 3 GHz. To get accurate measurements of resistance and reactance (impedance),
three different instrument set ups were used. From 10 Hz to 40 KHz, a home-built DSP-based vector network analyzer (VNA) [note 4]. From
50 kHz to 60 MHz an N2PK VNA was used [note 5].
And, finally, from 60 MHz to 3 GHz an HP8714B VNA measured impedance using the built-in bridge. The data from the various
instruments were transferred by files to the Gnumeric spread sheet program where a few calculations, such as magnitude of
impedance, were made and the graphs plotted.

All of the VNA arrangements listed also have provision for measuring 50-Ohm insertion loss and were used. Again, Gnumeric did the plotting of the graphs.

While the component data were in the spread sheet, they were converted to scattering-parameter files suitable for linear circuit analysis [note 6]. This is useful for constructing power filters on the computer and exploring various configurations.

**Conclusions and open questions -**
This note continues to support the case for the use of high capacity chip capacitors for
bypass and filtering applications. Anywhere from 1 to about 4 such components can be paralleled to increase
their effectiveness. The values can be chosen to suit the application, but should generally favor the high capacities.

As far as open questions, at VHF and higher frequencies, the series inductance of the chip caps is a limitation. Exploration of PC board layout schemes to minimize the added inductance could be useful. Some circuits only handle low amounts of DC current and here the ferrite beads can be replaced by resistors, reducing costs and improving performance. Multiple beads or resistors can be placed in series to improve the performance, taking advantage of the small chip size. These could be measured. There are difference in the circuit behavior of different ceramic materials, Z5V, X7R, etc. This includes changes with applied Voltage as well as temperature and should be investigated. One area of interesting study would be non-planar circuits that could mimic tubular feedthrough capacitors and their great performance at microwave frequencies. Along those lines is exploration of the construction of shielding to be used with the planar filters, such as discussed here.

Notes:

- Wes Hayward, W7ZOI, Rick Campbell, KK7B, and Bob Larkin, W7PUA,
*Experimental Methods in RF Design,*ARRL 2003. See section 2.8 on Bypass and Decoupling. - This bypass testing blog experimentally verifies the futility of using different values of capacitors in parallel. It also has useful comments and data on using vias to connect to the ground plane.
- The general article on MLCC capacitors in Wikipedia is excellent.
- Bob Larkin, W7PUA, "A DSP-Based Vector Network Analyzer for 10 Hz to 40 kHz," to be published in QEX.
- The N2PK vector network analyzer is a home-built project on the internet.
- Linear circuit models for the capacitors in this note are the simple series R-L-C . For the 330-Ohm ferrite bead, files are available using the Touchstone model and the ARRL RF Designer data.
- The behavior of the MLCC components can be better understood a detailed model of the structure. Information on this is in this description of chip cap inner workings

Last revised: 24 November 2017 - Copyright © *Robert Larkin 2017*