Unequal terminations place a lower limit on the attenuation as follows:. Express in decibels as:. If, as is typical, the attenuation is given in decibels K dB vs. An online attenuator calculator is provided at the bottom of the page. These equations apply to the two forms of Tee attenuators at the left. These equations apply to the two forms of Pi attenuators at the left.
Fixed Pi and Tee Attenuators - Equations
Note: Only enter values in the yellow cells or risk overwriting formulas! Attenuation: dB. An RF Cafe visitor wrote to say that he thought the above equations might be in error when unequal source and load termination resistances are used. The image below shows the mathematical steps that prove the equations are correct. Resistor values for both the "T" and ""Pi" attenuators were determined using the attenuator calculator on RF Cafe which uses these equations.
Its primary purpose was to provide me with ready access to commonly needed formulas and reference material while performing my work as an RF system and circuit design engineer.
The World Wide Web Internet was largely an unknown entity at the time and bandwidth was a scarce commodity. Dial-up modems blazed along at Unequal terminations place a lower limit on the attenuation as follows: Express in decibels as: In the attenuator formulas below:which is the linear attenuation ratio of the two powers or voltages note that "k" has a minimum value if Z 1 and Z 2. Unbalanced Tee T Attenuator. Tee Attenuator. Pi Attenuator.The Pi attenuator consists of one series resistor and two parallel shunt resistors to ground at the input and the output.
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Skin Depth Calculator. Stripline Impedance Calculator. Tank Circuit Resonance Calculator. Tee Attenuator Calculator. Temperature Converter. Torque Conversion Calculator.These voltage controlled attenuators often use PIN diodes and provide a variable level of attenuation dependent upon the voltage applied. The PIN diode variable attenuator is used to give attenuation over a range of about 20 dB and can be used in 50 ohm systems. The inductor L1 along with the capacitors C4 and C5 are included to prevent signal leakage from D1 to D2 that would impair the performance of the circuit.
The maximum attenuation is achieved when Vin is at a minimum. D3 is then reverse biased. When Vin is increased the diodes D1 and D2 become reverse biased, and D3 becomes forward biased, allowing the signal to pass through the circuit. These values are only a starting point for an experimental design, and are only provided as such.
The circuit may not be suitable in all instances. Although in theory almost any diode could be used in variable RF attenuators, PIN diodes have a number of advantages. This means that in their action as a radio frequency switch they do not create as many spurious products and additionally as an attenuator they have a more useful curve.
This PIN diode based voltage controlled variable attenuator is simple and easy to use. Variable attenuator circuit The PIN diode variable attenuator is used to give attenuation over a range of about 20 dB and can be used in 50 ohm systems.
Supplier Directory For everything from distribution to test equipment, components and more, our directory covers it. Featured articles.These RF attenuators can be fixed, switched or even continuously variable. Attenuators can also use a variety of different RF circuit design techniques: some used fixed resistors for fixed values of attenuators, others are switched, and other types may be variable using semiconductor technology to achieve this.
Whatever the technology and RF design techniques that are used, all attenuators serve to reduce the level of a signal, and surprisingly this can have many advantages in different situations. As the name implies RF attenuators reduce the level of the signal, i. Typically the attenuation is defined in decibels, and fixed attenuators may be available in a variety of levels. This attenuation may be required to protect a circuit stage from receiving a signal level that is too high.
Also an attenuator may be used to provide an accurate impedance match as most fixed attenuators offer a well-defined impedance, or attenuators may be used in a variety of areas where signal levels need to be controlled.
There are many uses for these RF attenuators and although they may not always seem obvious initially, they are widely used in RF circuit design applications and RF systems of different types. In some instances, RF attenuators may be required to reduce high levels of power and as a result they may need to incorporate a heatsink to ensure that the power can be suitably dissipated. It will be seen that some higher power RF attenuators incorporate a heatsink for this purpose.
Attenuators can be categorised in a number of ways according to their capabilities and the technologies they use:. They may come in a variety of formats from small in-line items in a similar format to connector adaptors to those in small boxes with connectors on the ends to those incorporated within equipment.
Fixed attenuators may even be be incorporated into the RF circuit design itself, possibly set out on the printed circuit board design. These fixed RF attenuators are easy to design and are seen in many circuit designs. Switched attenuators may also be found in items of test equipment to change the levels, for example of a signal generator output. Manually controlled RF attenuators will use ordinary manually controlled switched, but those that need to be controlled electronically can use reed relays, although PIN diodes can often be used.
There will always be some leakage across the switches, and for higher value attenuators, this can provide an inaccuracy. As a rule of thumb it is found that if the combined isolation of the switches isolation is 20 dB greater than the desired attenuation, the leakage through the isolated shorting path path will change the attenuation by no more than 1 dB.
It is theoretically possible to use standard switches for this type of attenuator, but in view of the fact that three switches are needed, FETs are typically used and it is this approach that is often adopted for RF attenuators used within MMIC or RFIC formats. Typically variable attenuators provide a continuous level change by varying an analogue voltage on the input control line.
These variable attenuators typically use soem form of voltage control that acts on a variable element like a PIN diode that works with other electronic components to provide a continuously variable level of attenuation. Continuously variable RF attenuators are normally used where accuracy is not a prime requirement, and where an analogue voltage is available.
They may be used in RF circuit design elements such as in feedback loops for controlling a level, or other similar applications. Each different type of RF attenuator is used in different circuit applications, and can provide the required performance. In fact the level of performance that can be achieved can be exceedingly high.
The different types of RF attenuator can be designed using different types of electronic component. Normally the type of RF attenuator dictates the type of components used. Fixed resistors are used and using these it is possible to provide accurate levels of attenuation, although the types of resistor used must not be inductive and the circuit layout must ensure that signal does not leak across each element.An attenuator is an electronic device that reduces the power of a signal without appreciably distorting its waveform.
An attenuator is effectively the opposite of an amplifierthough the two work by different methods. While an amplifier provides gainan attenuator provides loss, or gain less than 1. Attenuators are usually passive devices made from simple voltage divider networks. Switching between different resistances forms adjustable stepped attenuators and continuously adjustable ones using potentiometers. For higher frequencies precisely matched low VSWR resistance networks are used.
Fixed attenuators in circuits are used to lower voltage, dissipate power, and to improve impedance matching.
In measuring signals, attenuator pads or adapters are used to lower the amplitude of the signal a known amount to enable measurements, or to protect the measuring device from signal levels that might damage it.
These may be required to be balanced or unbalanced networks depending on whether the line geometry with which they are to be used is balanced or unbalanced. For instance, attenuators used with coaxial lines would be the unbalanced form while attenuators for use with twisted pair are required to be the balanced form.
Four fundamental attenuator circuit diagrams are given in the figures on the left. Since an attenuator circuit consists solely of passive resistor elements, it is both linear and reciprocal. If the circuit is also made symmetrical this is usually the case since it is usually required that the input and output impedance Z 1 and Z 2 are equalthen the input and output ports are not distinguished, but by convention the left and right sides of the circuits are referred to as input and output, respectively.
Various tables and calculators are available that provide a means of determining the appropriate resistor values for achieving particular loss values. Key specifications for attenuators are: .
Radio frequency attenuators are typically coaxial in structure with precision connectors as ports and coaxial, micro strip or thin-film internal structure. Above SHF special waveguide structure is required.
The size and shape of the attenuator depends on its ability to dissipate power. RF attenuators are used as loads for and as known attenuation and protective dissipation of power in measuring RF signals. A line-level attenuator in the preamp or a power attenuator after the power amplifier uses electrical resistance to reduce the amplitude of the signal that reaches the speaker, reducing the volume of the output.
This section concerns pi-pads, T-pads and L-pads made entirely from resistors and terminated on each port with a purely real resistance. The attenuator two-port is generally bidirectional. However, in this section it will be treated as though it were one way. In general, either of the two figures applies, but the first figure which depicts the source on the left will be tacitly assumed most of the time.
In the case of the L-pad, the second figure will be used if the load impedance is greater than the source impedance. The L-pad component value calculation assumes that the design impedance for port 1 on the left is equal or higher than the design impedance for port 2. Passive, resistive pads and attenuators are bidirectional two-ports, but in this section they will be treated as unidirectional.
If a source and load are both resistive i. Z 1 and Z 2 have zero or very small imaginary part then a resistive L-pad can be used to match them to each other. As shown, either side of the L-pad can be the source or load, but the Z 1 side must be the side with the higher impedance.This project arose from the fact that I had too much gain in my audio system, and I needed a practical solution without modifying the PCB circuit. There are very simple gadgets that can be used for audio purposes with great results.
These are passive attenuators. They are very simple objects based on a resistive partition housed in male-female RCA connectors and can be used in particular when there are differences in sensivity between the source CD player, preamp, etc. Despite the simple construction scheme, as I said before they can be quite expensive in the market.
Before proceeding further, we have to remember that the audio signal can be distinguished substantially in two categories:. The main difference between the two is that one is represented by an unshielded cable while the other does not. However, in reality the common RCA cable we use every day is made up of two conductors, one positive and one negative that also performs the shielding function against interferences provided that is not too long.
The outer casing consists of two pieces of an aluminum tube that can be purchased in any hardware store. I bought one one meter long tube and with a diameter just slightly greather than the RCA internal screw. Then I cut two equal pieces of cm long each. Then two wires cm in length are connected between the resistors and the terminals of the RCA connector. The two pieces can then also be painted at will as I did, by means of spray paint or left to its natural aluminium color.
The first to the signal pin while the second in parallel from signal to ground pin.
Voltage Controlled Variable RF Attenuator
You can choose the female connector for this operation, but the reverse is also fine. It is advisable to cover bare wires and resistors with shrink tubing and insulating tape. After this operation, the two resistors are interwoven and slightly soldered each other. At the end of the previous resistors, two electric wires cm long will be soldered and will then be connected to the ends of the other connector. At this point, the screw of each RCA connector is wound with the insulating tape so that it can fit perfectly inside the aluminum tube.
A little of cyanoacrylic glue guarantees the seal of the connector to the tube. Once the operation is done on one, the next one will be to solder the wires to the terminals of the other connector.
Finally, the second screw of the connector is fastened to the tube, always with the help of a little glue. Question 8 months ago. Is there a simple formula for calculating the apparent load impedance seen by the source? In my case I'm trying to maintain an input impedance of 10K ohm or greater to my CD player, while cutting its output voltage by over half.Archived from the original on January 14, 2013.
Retrieved June 6, 2012. Archived from the original on January 15, 2013.Pi Attenuator board build with JLCPCB
Jeffrey MacDonald (March 27, 2007). Archived from the original on May 23, 2017. The Emergence of the Modern World Conference, Otzenhausen, Germany: Penn State University. Archived from the original (PDF) on 9 November 2009. Retrieved 14 October 2009. Archived from the original on December 8, 2013. Retrieved September 17, 2017. Archived from the original on January 19, 2013.
Swords (1793) page 431: "The Beginning of the reign of Antichrist. Reader) are pretty well agreed that this reign is to be dated from about A. The Public Domain Review. Archived from the original on April 30, 2015. Journal of Evolution and Technology. Retrieved 10 September 2012. Geological Society of London. Archived from the original on July 10, 2012. Archived from the original on July 5, 2015. Monthly Notices of the Royal Astronomical Society.