905,761. Filters. STANDARD TELEPHONES & CABLES Ltd. May 1, 1959, No. 14957/59. Class 40 (8). An electric wave filter, Fig. 4, having narrow band - stop (or band - pass) characteristics in the neighbourhood of a frequency F comprises a first pair of terminals 1, 2 connected to the primary winding of a transformer 3 having a centre-tapped secondary winding, and a second pair of terminals 6, 7, one, 7, of which is connected to the centre tap and the other of which is connected to each of the terminals of the secondary winding through two respective impedance elements, one of which comprises an impedance network including resistive elements R 3 , R 4 and reactive elements C 1 , L 1 and C 2 , L 2 and piezo-electric crystal 13 which are resonant at the frequency F, the impedance network having the property that it presents an impedance substantially equal to a resistance R 1 outside the stop-band (or pass-band), and a substantially resistive impedance different from R 1 over the stop-band (or pass-band), and the other of which, R 2 , has a resistive impedance which is different from the impedance of the impedance network over a pass range of the filter and which is substantially the same as the impedance of the impedance network over a stop-range of the filter, The relationships between R 1 , R 2 , R 3 and R 4 for a band-stop filter and for a band-pass filter are stated. In the construction shown in Fig. 5, the piezo-electric crystal 13 is omitted and a piezo-electric narrow band-pass filter 19 is connected in series with L 1 , C 1 . The filter 19 has characteristic impedance R 5 and is terminated by a resistor R 5 . The pass-band of the filter 19 is centred on the frequency F and presents to the network an impedance which is substantially zero outside the pass-band. The relationships between R 1 , R 2 , R 4 and R 5 for a band-stop filter, and for a band-pass filter are stated. In the construction of a narrow stopband filter, shown in Fig. 6, the impedance networks 21A, 21B each comprise two equal series-connected resistors of value R 1 for the first impedance network and of value R 2 for the second impedance network, one of the resistors 22A, 22B of each network being shunted by a parallel-resonant circuit 17A, 18A, 17B, 18B resonant at the frequency F, and the other resistor 23A, 23B of each network being shunted by a series-resonant circuit 15A, 16A, 15B, 16B resonant at the frequency F, and which is the inverse with respect to R 1 or R 2 of the respective parallel-resonant circuit, and a sharply resonant piezo-electric device 13A, 13B connected to shunt the parallel-resonant circuit, the device 13A, 13B being series resonant at the frequency F. In this construction both networks have substantially zero impedance. In an alternative form of filter with a narrow stopband the networks 21A and 21B of Fig. 6 are each replaced by the network 24 of Fig. 7, the resistors 9 and 10 of the network 24 having the value R 1 when it replaces the network 21A in Fig. 6, and the value R 2 when it replaces the network 21B, and both impedance networks having substantially infinite impedance at the frequency F. Fig. 8 shows a filter with a narrow pass-band in which the network 21B of Fig. 6 is replaced by the network 24 of Fig. 7, both resistors 9 and 10 having the same value R 1 as the resistors 22A and 23A in the network 21A. The filter has substantially infinite attenuation except at the frequency F, when network 21A has zero impedance and network 24 has infinite impedance. In order to minimize the effect of spurious resonances in the piezo-electric crystals used in the above circuits each crystal can be replaced by a group of crystals all having the same principal resonance frequency but with non-coincident spurious resonance frequencies. In the arrangement of Fig. 5 the effect can be minimized by increasing the value of L 1 /R 4 . In the case of band-stop filters the effect can be minimized as shown in Fig. 9, the inductor 17 (L 2 ) of Fig. 4 being provided with a centre-tap and two piezo-electric crystals 13X and 13Y replacing the crystal 13. Both crystals 13X and 13Y resonate at the frequency F and both have half the impedance of the crystal 13, but have different spurious resonance frequencies. The resistor 31 has a resistance equal to half the impedance at frequency F of the effective shunting capacity of each crystal.