Resonant tank circuits

Quasi-resonant converters are a separate class of switching power supplies that tune the ac power waveforms to reduce or eliminate the switching loss within the supply. This is done by placing resonant tank circuits within the ac current paths to create pseudo-sinusoidal voltage or current waveforms. Because the tank circuits have one resonant frequency, the method of control needs to be modified to a variable frequency control where the resonant period is fixed and the control varies the period of the non-resonant period. The quasi-resonant converters usually operate in the 300 kHz to 2 MHz frequency range. 

Figure 4-15 The two methods of loading a resonant tank circuit.

Fig. 2.5.3 Typical NMR resonant tank circuit, showing coil loss mechanisms. This LC circuit is then placed in series with two matching capacitors (Cmatch). The resistance of the circuit is represented by Rco], the inductive losses by Rm and the dielectric losses by Ci, Cd and Rd.

The RF SQUID is based on the AC Josephson effect, uses only one Josephson junction, and is less sensitive than the DC SQUID, but is cheaper and easier to manufacture its SQUID is inductively coupled to a resonant tank circuit. Depending on the external magnetic field, as the SQUID operates in the resistive mode, the effective inductance of the tank circuit changes, thus changing the resonant frequency of the tank circuit. These frequency measurements can be easily done, and thus the losses that appear as the voltage across the load resistor in the circuit are a periodic function of the applied magnetic flux with a period of 0. 

The impedance at resonance can be changed by changing the L-C combination while satisfying the resonance condition. Therefore, a parallel resonance tank circuit can match the impedance of the coil to that of the rest of the circuit with just one additional component, namely a tuning capacitor. This is simpler and more efficient than schemes having more components. [But with a given coil the tank can have a... 

For building probes, making tank circuits, and as an rf source which acts as a artificial NMR signal without any electrical connections to the circuit, a dip meter is nearly essential. In addition, it is useful in its intended role to passively measure the parallel resonant tank circuit s resonant frequency... 

No capacitor is needed for the resonant tank circuit, because the "distributed capacitance" of the coil and other wires (sometimes called "stray capacitance") is sufficient for resonating at about 1 MHz. 

The coil of the resonant tank circuit, as usual in this course, has been simplified beyond the limits of what many people would believe might work, and yet it does work rather well. It is a reel of "hook-up wire," with an inside diameter of one inch and about 2 inches outside diameter. The coil is about 1/2 inch in "length" as defined on page 114. It is wound on a reel made of plastic. The length of the wire if completely uncoiled is 75 feet. 

In the first chapter, a very primitive radio transmitter was described, and it was mentioned that it was similar to the one on the famous ship Titanic. The transmitter shown in Fig. 19.2 is closer to the Titanic s radio, because it has a capacitor in parallel with the inductor, making a tuned resonant tank circuit (see index if necessary). This concentrates the transmissions at one particular frequency range. Also, the oscillating relay repeats those transmissions automatically. If an antenna were connected, as on page 181, the radio waves could be heard on an AM radio farther away. 

Quasi-resonant converters utilize an T-C tank circuit, which rings at its natural resonance frequency in response to a step change in its terminal voltage or current. The tank circuit is placed between the power switch and the transformer and/or the transformer and the output filter. 

Frequency limiting is also provided on all the resonant controllers on the market today. The resonant frequency of the tank circuit is given by... 

Next, decide the natural resonance frequency of the tank circuit. For the available quasi-resonant controller ICs on the market, the range is between 1 and 2 MHz. This limit should be considered the maximum limit within conventional QR designs. So 1 to 1.5 MHz is a typical choice. Lower frequencies can be used and some efficiencies can be gained. The equation for the resonance frequency is... 

It is desired that the resonanee frequency of the tank circuit be 1 MHz. In ZVS QR converters, the tank circuit is not responsible for storing and passing on energy as it is in ZCS QR converters. The tank circuit can be seen more as an off-time transition shaper similar to a snubber when used in PWM converters. Here a wide range of values for both the inductor and the capacitor will work as long as their combined resonant frequency is 1 MHz or... 

For signal enhancement we use superconducting tank circuits attached to the correction electrodes (some are splitted to allow detection of the radial motion). The resonance frequencies of the circuits are tuned to the corresponding ion oscillation frequencies. 

In a similar way also the cyclotron motion can be cooled and detected when the tank circuit connecting two segments of the splitted correction electrode is kept in resonance with the ions cyclotron frequency. Fig. 5 shows an example for resistive cooling of the cyclotron motion of a single 12( 5+ calibration... 

The resonance frequency of mixer-amplifier tank circuit is measured to be 1.5 GHz. The SQUID amplifier has the following experimentally measured parameters critical current and normal state resistance per junction of front end SQUID are Ic=40 pA and Rn=4 Q, squid inductance is 40 pH, mutual input inductance is 400 pH and input inductance is 5 nH providing the amplifier noise temperature Tn=90 K. 

Fig. 13. a) A schematic of the LC-tank circuit used to transform the high impedance of the RF-SET down to the characteristic impedance of Z = 50 Q. h) Using the simulation software ADS, Sn is plotted for the case when Rrf-set = 100 kQ (hrown) and when it is 130 kQ (green) along with the corresponding Smith chart, (c). The simulated component values of the tank circuit were Cpamsitk =0.18 pF, Ltank = 710 nH, and the resistance of the inductor at its resonant frequency Rk-rank = 10... 

Once the coil has been incorporated into a tank circuit, a dip meter can be used to measure the resonance frequency. For a parallel resonant circuit, the dip meter can be used in the usual way, i.e., look for a "dip" indication as a function of frequency. For a series tank circuit, it is best to use the dip meter as an rf source acting like an artificial NMR signal and maximize the receiver output when the receiving system is fully hooked up. This will work also for the parallel tank. (See section V.C.9. on impedance matching.)... 

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