Capacitor-input filter

A resonant transformer, also Boucherot circuit is a resonant circuit like circuit of capacitor and coil to reach a predetermined frequency power matching between components or modules. At low frequency applications, ferrite cores can be used to strengthen the magnetic field in the coil. Normally deleted at high frequency applications, however, the iron core of the coil, as it distorts the transformed AC voltage by its physical characteristics, and limits the performance.

General

A resonant transformer, like any transformer transform both voltage and current, but has ( as an autotransformer ) no galvanic isolation, and only works in a narrow frequency band. It will therefore only be used when the frequency does not change significantly.

In order to achieve low transmission losses and good efficiency broadband transformers require a fairly good magnetic coupling of all the coils. At low frequencies, this can be achieved with a common high permeability iron core also reduces the number of turns of the coils. However, the iron losses increase so strong that you can only use air coils in the high frequency range for frequencies above about 1000 Hz. Their disadvantage is the low magnetic coupling of all windings, but this is not detrimental if one uses the resonance effect of the resonant circuit for the transformation. Since air coils can not be magnetically saturated, the transmittable power is theoretically unlimited.

A particular advantage of the resonant transformer, the low-pass effect, which reduces the harmonic content of the transmitted signal.

Calculation

Determining the values ​​of the inductor L and capacitor C for the purpose of power adjustment to correspond to the amounts of the external resistors R1 and R2 on either side of the impedances of the resonant transformer.

Power adjustment means that, in the above circuit, with exemplary resistance values ​​for R1 and R2 either

• A source ( left) with the internal resistance R2 = 30 Ω as much power to the load R1 = 140 Ω to leave or
• A source ( right) with the internal resistance R1 = 140 Ω as much power to the load R2 = 30 Ω to leave.

In both cases, the value of the consumer by a certain factor is enlarged or reduced with respect to the value on the other side of the red image framed resonance transformer.

The dimensioning of the resonance transformer can be made either with a Smith chart graphically or mathematically as described below in the context of the complex AC circuit analysis. The Kirchhoff's rules, and the laws of series and parallel circuits apply. The inductive impedance ZL of the inductor L with the angular frequency ω = 2 · π · f is given by

And the capacitive impedance Zc of the capacitor C

For the equivalent resistance Zgesamt two parallel connected resistors is generally

Applying this formula to the parallel connection of R1 and C. concerns

With the auxiliary variable Q = R1ωC, the quality factor. For the equivalent resistance of a series circuit you have to add up the individual resistances; in this case, it follows

For performance adjustment applies to this ( shown above) circuit

This complex equation decomposes at known values ​​of ω, R1 and R2 in two real defining equations for L and C, since the imaginary part of the right side of the equation must be zero. The solutions are:

Example: Modification of power in the image is to be calculated for the frequency of 100 MHz. This is Q = 1.915; C = 22 pF and L = 91 nH.

Example: Fitting a dipole antenna

The input impedance of a dipole depends strongly on the location of the feed. One separates the dipole, and includes therein a balanced cable, one must design the impedance of about 74 Ω in order to achieve impedance matching. If the dipole ( as in the picture ) is not interrupted in the middle, you can feed the power asymmetrically at one end. With thin wire antennas is measured at this point has an impedance of about 2200 Ω. As a rule, the radio station with the antenna via an unbalanced coaxial cable impedance 75 Ω or 50 Ω is connected, therefore, a low-loss transformer must be interposed in order to prevent excessive mismatch. Since a dipole antenna has only a relatively low bandwidth from a few percent of the center frequency, a narrow band resonant transformer is very suitable for the impedance matching.

For a frequency of 3.6 MHz and a 50 - Ω cable in the following values ​​:

This circuit has over the otherwise conventional feed the " current loop " in the dipole some advantages:

• The resonant frequency of the antenna can be moved by slight deviation from C or L to about 10 % of the calculated values ​​without the standing wave ratio inadmissible assumes large values. Which corresponds to an increased bandwidth of the antenna.
• The resonant transformer is easily accessible at the end of the antenna mounted.
• For long wire antennas hangs in the dipole no heavy coax with balun.

One disadvantage is you view that in the end feed at higher impedance input supply voltage, the course is higher (in this example by a factor of 6.56 ). The peak voltage increases at P = 100 W then from 100 V to 656 V. This must be taken into account when dimensioning the component.

PI filter

In the high-frequency technology is operated preferably power transistors and vacuum tubes as switches (C- mode) in order to avoid unnecessary loss of heat through high efficiency. According to the laws of fourier analysis result by an abrupt turning on and off a voltage many harmonics, radiated and interfere with the operation of other devices. To prevent this, the low-pass filters, the resonant circuits or resonant transformers sufficiently high Q to be installed. A rule of thumb is that as Q ≥ 8, the harmonics of the AC voltage can be sufficiently suppressed.

In the resonant transformers just described, simple Q depends only on the ratio of the resistors to the input and output. If the resistors have approximately the same value Q is too small, to ensure significant filtering effect. This can be changed by combination of two resonant transformers. The circuit is reminiscent of the Greek letter π, therefore, the term pi filter prevailed. Sometimes also the name Collins filter is used because it has been known for her good qualities in radios of the same company Rockwell Collins.

The calculation of the components is done in two stages: The resistor R2 is transformed down by C2 and L2 to a very low intermediate value R3 ≈ 1 Ω, which you can think of at the junction of the two red rectangles. R3 is not available as a component, but this fictitious intermediate value is transformed by C1 and L1 to the desired resistance R1. Since both transformers have a high resonance quality factor Q, the desired filtering effect is achieved.

A change in the calculated number of turns is required when L1 and L2 are usually combined into a single coil - both reels the number of turns is n is then magnetically coupled, and the total number of turns has to resonance, depending on the coil form has a value k · n 2 > k> 20, 5, so that a total inductance L1 L2 results.

Applications

Applications is the resonant transformer in a variety of areas. Below are some application areas are listed as examples.

• In radios and radio-frequency technology is used formed from resonance transformers band filters that transmit a narrow frequency range of an amplifier stage to the next. This includes for example: certain types of balun for matching the characteristic impedance of a cable by means of an antenna ( impedance transformation).
• Matching between two successive amplifier stages ( transistors).

• For the transmission of electric power in the form of special switching power supplies, resonant converters for converting between different voltage levels: For the operation of cold cathode tubes for flat screens or in electronic ballasts for compact fluorescent lamps and energy saving lamps to produce the necessary operating voltage of the tubes. It is typical that automatically provide these converters with a not yet ignited cold cathode tube due to the high output impedance then the required high ignition voltage. It is formed when operated on low voltage and for electrical isolation of the resonant transformer with a real transformer.
• In television receivers with cathode-ray tube, the necessary power for the line deflection flyback transformer operates at a resonant flyback converter, and then generates the anode voltage of the picture tube.
• In the quasi-resonant switching power supplies, see the switching transitions as a resonant half-wave instead; so that the switching losses can be reduced drastically.
• The Tesla transformer produced by resonance voltages over 100 kV.