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A double-tuned transformer from a radio receiver intermediate-frequency amplifier with its screening can removed. A double-tuned amplifier is a tuned amplifier with transformer coupling between the amplifier stages in which the inductances of both the primary and secondary windings are tuned separately with a capacitor across each.
Note, , the reactance in parallel, has a negative reactance because it is typically a capacitor. This gives the L-network the additional feature of harmonic suppression since it is a low pass filter too. The inverse connection (impedance step-up) is simply the reverse—for example, reactance in series with the source.
One of the windings of the transformer had a variable capacitor connected across it to make a tuned circuit. A variable capacitor (or sometimes a variable coupling coil called a variometer) was used, with a knob on the front panel to tune the receiver. The RF stages usually had identical circuits to simplify design.
Perfect coupling implies infinitely high core magnetic permeability and winding inductance and zero net magnetomotive force (i.e. i p n p − i s n s = 0). [3] [c] Ideal transformer connected with source V P on primary and load impedance Z L on secondary, where 0 < Z L < ∞. Ideal transformer and induction law [d]
The coupling factor is defined as: , = where P 1 is the input power at port 1 and P 3 is the output power from the coupled port (see figure 1). The coupling factor represents the primary property of a directional coupler.
Fig. 1 L P σ and L S σ are primary and secondary leakage inductances expressed in terms of inductive coupling coefficient under open-circuited conditions.. The magnetic circuit's flux that does not interlink both windings is the leakage flux corresponding to primary leakage inductance L P σ and secondary leakage inductance L S σ.
Other transformer parameters like leakage inductance and mutual inductance which cannot be directly measured may be defined in terms of k. Short-circuit inductance is one of the parameters that determines the resonance frequency of the magnetic phase synchronous coupling in a resonant transformer and wireless power transfer.
The corollary problem, to find a synthesis of PRFs using R and C elements with only one inductor, is an unsolved problem in network theory. [31] Another unsolved problem is finding a proof of Darlington's conjecture (1955) that any RC 2-port with a common terminal can be realised as a series-parallel network. [ 32 ]