<Dd> f = 1 2 π L C (\ displaystyle f = (1 \ over 2 \ pi (\ sqrt (LC))) \,) </Dd> <P> In order to reject radio noise and interference from other transmitters near in frequency to the desired station, the bandpass filter (tuned circuit) in the receiver has to have a narrow bandwidth, allowing only a narrow band of frequencies through . The form of bandpass filter that was used in the first receivers, which has continued to be used in receivers until recently, was the double - tuned inductively - coupled circuit, or resonant transformer (oscillation transformer or RF transformer). The antenna and ground were connected to a coil of wire, which was magnetically coupled to a second coil with a capacitor across it, which was connected to the detector . The RF alternating current from the antenna through the primary coil created a magnetic field which induced a current in the secondary coil which fed the detector . Both primary and secondary were tuned circuits; the primary coil resonated with the capacitance of the antenna, while the secondary coil resonated with the capacitor across it . Both were adjusted to the same resonant frequency . </P> <P> This circuit had two advantages . One was that by using the correct turns ratio, the impedance of the antenna could be matched to the impedance of the receiver, to transfer maximum RF power to the receiver . Impedance matching was important to achieve maximum receiving range in the unamplified receivers of this era . The coils usually had taps which could be selected by a multiposition switch . The second advantage was that due to "loose coupling" it had a much narrower bandwidth than a simple tuned circuit, and the bandwidth could be adjusted . Unlike in an ordinary transformer, the two coils were "loosely coupled"; separated physically so not all the magnetic field from the primary passed through the secondary, reducing the mutual inductance . This gave the coupled tuned circuits much "sharper" tuning, a narrower bandwidth than a single tuned circuit . In the "Navy type" loose coupler (see picture), widely used with crystal receivers, the smaller secondary coil was mounted on a rack which could be slid in or out of the primary coil, to vary the mutual inductance between the coils . When the operator encountered an interfering signal at a nearby frequency, the secondary could be slid further out of the primary, reducing the coupling, which narrowed the bandwidth, rejecting the interfering signal . A disadvantage was that all three adjustments in the loose coupler - primary tuning, secondary tuning, and coupling - were interactive; changing one changed the others . So tuning in a new station was a process of successive adjustments . </P> <P> Selectivity became more important as spark transmitters were replaced by continuous wave transmitters which transmitted on a narrow band of frequencies, and broadcasting led to a proliferation of closely spaced radio stations crowding the radio spectrum . Resonant transformers continued to be used as the bandpass filter in vacuum tube radios, and new forms such as the variometer were invented . Another advantage of the double - tuned transformer for AM reception was that when properly adjusted it had a "flat top" frequency response curve as opposed to the "peaked" response of a single tuned circuit . This allowed it to pass the sidebands of AM modulation on either side of the carrier with little distortion, unlike a single tuned circuit which attenuated the higher audio frequencies . Until recently the bandpass filters in the superheterodyne circuit used in all modern receivers were made with resonant transformers, called IF transformers . </P>

Which type of diode is used in radio receivers