Abstract:
The present invention provides a means for improving the sensitivity and selectivity of a car radio receiver. The variable inductance LC resonant circuit comprises: a amplifier  53  having enough high input impedance and enough low output impedance, a inductive element  51  connected a terminal to the input of said amplifier  53  and the other terminal to the output terminal of said amplifier  53 , and a capacitive element  52  connected a terminal to the input terminal of said amplifier  53  and the other terminal to the ground. The proposed technique alters the parallel resonant frequency by varying an equivalent inductance  51, 53  seen from the condenser  52  side, wherein the equivalent inductance  51, 53  varies associated with the gain of said amplifier depending on the frequency control voltage from the PLL synthesizer to the terminal  54.

Description:
[0001]    This application is related to application number 2006-92244, filed Mar. 2, 2006, in Japan, the disclosure of which is incorporated herein by reference and to which priority is claimed. 
         [0002]    The present invention relates to a variable inductance LC resonant circuit, which has a wide variable frequency range operates with low voltage and is fundamental and to be improved for realizing the radio receiver with high sensitivity and selectivity. 
       BACKGROUND OF THE INVENTION 
       [0003]    First, the biggest problem for a car radio frequency bands, such as, LW (Long Wave) band and MW (Middle Wave) band commonly called AM (amplitude Modulation) band, SW (Short Wave) band, and the like is not available a tuning circuit at the front end of an antenna because of the own condition imposed on the antenna of the car radio. 
         [0004]    The resonant circuit of the prior art comprises inductors with fixed inductances and variable capacitance diodes. The variable capacitance range of the variable capacitance diode is 25 to 500 pF at 8 volts, which corresponds to the variable frequency ratio of about 4.5. With this variable range, it is enough to cover at least the AM band of 522 to 1710 kHz. 
         [0005]    However, a car antenna has high impedance since it is composed of very short elements compared with receiving wave length, and as the antenna must be connected to a receiver via a coaxial cable of 1 m legally, the equivalent circuit of the antenna should be illustrated in  FIG. 1 . In  FIG. 1 , a symbol  11  indicates electromotive force generated in the antenna, a symbol  12  indicates antenna resistance of 75 ohms, a symbol  13  indicates antenna capacitance of 15 pF, and a symbol  14  indicates cable capacitance of 65 pF. These values are determined internationally in order to keep compatibility between a radio receiver and a car radio antenna. 
         [0006]    This means that, seen from the front end of the tuning circuit of receiver, totally 80 pF capacitance consisted of the antenna capacitance of 15 pF and the cable capacitance of 15 pF is added to the tuning circuit, and, equivalently, the variable capacitance range changes to 105-580 pF, which leads to the decrease in the variable capacitance ratio to at most 6. Converting this to the variable frequency ratio, it is compressed to about 2, correspondingly, the tuning circuit in the antenna stage can not cover even the AM band. 
         [0007]    Therefore, a method is adopted in which, as shown in  FIG. 2 , a plurality of coils are provided, and a frequency variable range is widen by switching the coils depending on the receiving frequency. In  FIG. 2 , a symbol  21  indicates coils, a symbol  22  indicates variable capacitance diodes, a symbol  23  indicates a buffer resistance, a symbol  24  indicates switches, a symbol  25  indicates control signal output via switches, and a symbol  26  indicates a terminal for inputting frequency control voltage from PLL (Phase Locked Loop) synthesizer. 
         [0008]    In a coil-switching scheme that covers the frequency bands with, for example, three tuning circuits at the front end and a local signal generator with a resonant circuit, by switching each two coils included in each circuit, totally even  8  coils are necessary, that inevitably leads to large system size. 
         [0009]    However, as various optional systems such as cassette tape recorder, CD (Compact Disc) driver, MD (Mini disc, Trade Mark) driver, and the like are mounted on the same car radio, miniaturization is also necessary to the car receiver, and the coil switching scheme becomes useless as being inadequate to miniaturization. 
         [0010]    As a result, the tuning circuit in the antenna stage is omitted and the RF amplifier with high input impedance directly receives signals from the antenna, which sacrifices high sensitivity and selectivity characteristics which are the most important performances for a receiver. 
         [0011]    A typical front end of a radio receiver of the prior art is shown in  FIG. 3 . A block surrounded a broken line shown in  FIG. 1  indicates an equivalent circuit of an antenna, a symbol  15  indicates a RF amplifier, symbols  16  and  17  indicate a tuning circuit respectively, a symbol  18  indicates a RF mixer, a symbol  19  indicates a local signal generator, a symbol  30  indicates a terminal for outputting an intermediate frequency signal, a symbol  31  indicates voltage supplied for tuning from the PLL synthesizer, and a symbol  32  indicates a choke coil with a fixed inductance which has a resonance frequency near 300 kHz together with the total 80 pF consisted of antenna capacitance of 15 pF and cable capacitance of 65 pF and is provided in order to attenuate the hum with frequencies of 50 and 60 Hz from the High voltage transmission line. Variable tuning circuits are merely provided with at the rear stage and not provided in the front stage at all. Therefore, the antenna stage is, as can be seen from  FIG. 4 , ineffective to reject undesired signals at all. 
         [0012]    The loss caused by the lack of a tuning circuit in the antenna stage is estimated actually to about −20 dB, which consists of about −15 dB originated from voltage division between antenna capacitance 15 pF and distributed capacitance 65 pF of coaxial cable and the contributions from the presence of a stray capacitance between the respective coils of the choke coil for reducing the hum from high voltage transmission line, an input capacitance of RF amplifier, and the like. 
         [0013]    The receiver of the prior art, which inevitably abort the high capability of undesired signal rejection at the antenna stage, causes cross-talk under the presence of undesired high power signals by the overload of a RF amplifier. In order to avoid the problem, for a certain type of receiver, the gain at the antenna stage is strongly suppressed by AGC (Automatic Gain Controller), which results in the occurrence of the so-called sensitivity oppression that simultaneously suppresses the desired signal. 
       SUMMARY OF THE INVENTION 
       [0014]    It is an object of the present invention to provide a variable tuning circuit with high sensitivity and selectivity and a radio receiver with the same in the antenna stage, which resolve disadvantages associated with the radio receiver of the prior art. 
         [0015]    In accordance with the invention, a variable inductance LC resonant circuit is provided, comprising a amplifier having enough high input impedance and enough low output impedance, a inductive element connected a terminal to the input of said amplifier and the other terminal to the output terminal of said amplifier, and a capacitive element connected a terminal to the input terminal of said amplifier and the other terminal to the ground; wherein resonant frequency of said resonant circuit is variable by changing the gain of said amplifier less than +1. 
         [0016]    In another aspect of the present invention, a radio receiver with high sensitivity and high selectivity is provided by using the variable inductance LC resonant circuit described above. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0017]      FIG. 1  shows an equivalent circuit of an antenna. 
           [0018]      FIG. 2  shows a coil switching scheme of the prior art. 
           [0019]      FIG. 3  show a typical front end of a radio receiver of the prior art. 
           [0020]      FIG. 4  shows a typical property of an antenna stage of the prior art. 
           [0021]      FIG. 5  shows an embodiment of a variable inductance LC resonant circuit of the present invention. 
           [0022]      FIG. 6  shows an equivalent circuit of the variable inductance LC resonant circuit of the present invention. 
           [0023]      FIG. 7  shows an equivalent circuit of the circuit shown in  FIG. 6 . 
           [0024]      FIG. 8  shows an equivalent circuit of the resonant circuit shown in  FIG. 6  with an external load. 
           [0025]      FIG. 9  shows a feedback path of the variable inductance LC resonant circuit of the present invention. 
           [0026]      FIG. 10  shows a Nyquist locus of the variable inductance LC resonant circuit of the present invention. 
           [0027]      FIG. 11  shows an embodiment of a variable gain amplifier used in the variable inductance LC resonant circuit of the present invention. 
           [0028]      FIG. 12  shows an embodiment of a pre-amplifier included in the variable gain amplifier used in the variable inductance LC resonant circuit of the present invention. 
           [0029]      FIG. 13  shows an embodiment of a post-amplifier included in the variable gain amplifier used in the variable inductance LC resonant circuit of the present invention. 
           [0030]      FIG. 14  shows an example of the variable range of the variable inductance LC resonant circuit of the present invention. 
           [0031]      FIG. 15  shows the other embodiment of the variable inductance LC resonant circuit of the present invention. 
           [0032]      FIG. 16  shows embodiments of both a tap coupling and secondary coil coupling for the use of the variable inductance LC resonant circuit of the present invention as a tuning circuit. 
           [0033]      FIG. 17  shows an embodiment of an oscillator with the variable inductance LC resonant circuit of the present invention. 
           [0034]      FIG. 18  shows an embodiment of sharing the pre-amplifier of the variable inductance LC resonant circuit of the present invention with a RF amplifier having AGC function. 
           [0035]      FIG. 19  shows an embodiment of sharing the pre-amplifier of the variable inductance LC resonant circuit of the present invention with a RF mixer. 
           [0036]      FIG. 20  shows a typical radio receiver of the prior art. 
           [0037]      FIG. 21  shows an embodiment of a radio receiver of the present invention. 
       
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
       [0038]    Referring now to the drawings, the embodiment of the variable inductance LC resonant circuit in accordance with the present invention is explained in detail. The principle of the variable inductance LC resonant circuit of the present invention is now explained by referring to a circuit shown  FIG. 5 . In  FIG. 5 , a symbol  51  indicates a coil with inductance L, a symbol  52  indicates a capacitor with capacitance C, a symbol  53  indicates an amplifier having enough high input impedance and enough low output impedance and gain G variable electrically in the range of less than +1, and a symbol  54  indicates frequency control signal from PLL synthesizer. 
         [0039]    Hereat, the circuit shown in  FIG. 5  becomes equivalent to the one shown in  FIG. 6  in the limit of infinitely high input impedance and infinitely low output impedance of the amplifier. The principle of the variable inductance LC resonant circuit is explained which is elementally equivalent to that of the present invention. The current i c  flowing through the capacitor with capacitance C is expressed by Formula (1), and the current i L  flowing through the coil with inductance L is expressed by Formula (2); 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       i 
                       c 
                     
                     = 
                     
                       jω 
                        
                       
                           
                       
                        
                       
                         C 
                         · 
                         
                           v 
                           i 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     1 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         
                           i 
                           L 
                         
                         = 
                           
                          
                         
                           
                             
                               v 
                               i 
                             
                             - 
                             
                               v 
                               o 
                             
                           
                           
                             jω 
                              
                             
                                 
                             
                              
                             L 
                           
                         
                       
                     
                   
                   
                     
                       
                         
                           = 
                             
                            
                           
                             
                               
                                 1 
                                 - 
                                 G 
                               
                               
                                 jω 
                                  
                                 
                                     
                                 
                                  
                                 L 
                               
                             
                             · 
                             
                               v 
                               i 
                             
                           
                         
                         , 
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     2 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    where j indicates sqrt(−1), v i  indicates input voltage, v o  indicates output voltage, omega. indicates angular frequency (=2×.pai.×frequency). Therefore, the admittance Y in  of the parallel resonant circuit is expressed by the following formula (3). 
         [0000]    
       
         
           
               
             
               
                 
                   
                     
                       
                         
                           
                             Y 
                             
                               in 
                             
                           
                           = 
                             
                            
                           
                             
                               
                                 i 
                                 c 
                               
                               + 
                               
                                 i 
                                 L 
                               
                             
                             
                               v 
                               i 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               ( 
                               
                                 
                                   jω 
                                    
                                   
                                       
                                   
                                    
                                   
                                     C 
                                     · 
                                     
                                       v 
                                       i 
                                     
                                   
                                 
                                 + 
                                 
                                   
                                     
                                       1 
                                       - 
                                       G 
                                     
                                     
                                       jω 
                                        
                                       
                                           
                                       
                                        
                                       L 
                                     
                                   
                                   · 
                                   
                                     v 
                                     i 
                                   
                                 
                               
                               ) 
                             
                             / 
                             
                               v 
                               i 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               jω 
                                
                               
                                   
                               
                                
                               C 
                             
                             + 
                             
                               
                                 1 
                                 - 
                                 G 
                               
                               
                                 jω 
                                  
                                 
                                     
                                 
                                  
                                 L 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               jω 
                                
                               
                                   
                               
                                
                               C 
                             
                             + 
                             
                               1 
                               / 
                               
                                 ( 
                                 
                                   
                                     jω 
                                      
                                     
                                         
                                     
                                      
                                     L 
                                   
                                   
                                     1 
                                     - 
                                     G 
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               jω 
                                
                               
                                   
                               
                                
                               C 
                             
                             + 
                             
                               1 
                               
                                 jω 
                                  
                                 
                                     
                                 
                                  
                                 
                                   L 
                                   ′ 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     
                       Formula 
                        
                       
                           
                       
                        
                       3 
                     
                     ) 
                   
                 
               
             
           
         
       
     
       Herein virtual inductance L is expressed as follows. 
       [0040]    
       
         
           
             
               
                 
                   
                     L 
                     ′ 
                   
                   = 
                   
                     L 
                     
                       1 
                       - 
                       G 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     4 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    It is clear from the formula (3) that the circuit shown in  FIG. 5  is a parallel resonant circuit equivalent to that shown in  FIG. 7 . In  FIG. 7 , a symbol  71  indicates a coil with inductance L′ described in the formula (4), a symbol  72  indicates a capacitor with the same capacitance marked by a symbol  52  in  FIG. 5 . 
         [0041]    Furthermore, the equivalent circuit changes to that shown in  FIG. 8  in case of presence of an external load and a loss resistance associated with the coil. 
         [0042]    Defining the resonant angular frequency omeg.sub. 0  by using a fixed inductance L and fixed capacitance C, the resonant angular frequency omega.sub.r of the variable inductance LC resonant circuit is expressed by formula (5), and this formula shows that the resonant angular frequency omega..sub.r is variable, in principle, from zero to infinity as the gain of an amplifier is altered from +1 to −.inf.Practically, the resonant angular frequency omega.sub.r is variable from zero to .omeg.sub. 0 , since the gain G is easily changeable from +1 to zero. 
         [0000]    
       
         
           
               
             
               
                 
                   
                     
                       
                         
                           
                             ω 
                             r 
                           
                           = 
                             
                            
                           
                             1 
                             
                               
                                 
                                   L 
                                   ′ 
                                 
                                  
                                 C 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             1 
                             / 
                             
                               
                                 
                                   L 
                                   
                                     1 
                                     - 
                                     G 
                                   
                                 
                                 · 
                                 C 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               
                                 1 
                                 - 
                                 G 
                               
                             
                             
                               LC 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                             
                            
                           
                             
                               ω 
                               0 
                             
                              
                             
                               
                                 1 
                                 - 
                                 G 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     
                       Formula 
                        
                       
                           
                       
                        
                       5 
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    The variable inductance LC resonant circuit of the present invention includes a feedback circuit with an amplifier. The variable inductance LC resonant circuit oscillates when the feedback path has an inadequate phase vs. amplitude performance. However, the variable inductance LC resonant circuit according to the present invention has a stable feedback path, which can be proved as described below by applying the Nyquist stable criterion. 
         [0043]    In  FIG. 9 , a symbol  91  indicates a coil with inductance L, a symbol  92  indicates a condenser with capacitance C, a symbol  93  indicates a load resistance R, and a symbol  94  indicates a variable gain amplifier with a gain less than +1. A feedback constant beta. of the feedback path and loop gain G.beta. are expressed by the following formulae (6) and (7). 
         [0000]    
       
         
           
               
             
               
                 
                   
                     
                       
                         
                           β 
                           = 
                           
                             
                               ( 
                               
                                 1 
                                 / 
                                 
                                   ( 
                                   
                                     
                                       jω 
                                        
                                       
                                           
                                       
                                        
                                       C 
                                     
                                     + 
                                     
                                       1 
                                       R 
                                     
                                   
                                   ) 
                                 
                               
                               ) 
                             
                             / 
                             
                               ( 
                               
                                 
                                   jω 
                                    
                                   
                                       
                                   
                                    
                                   L 
                                 
                                 + 
                                 
                                   1 
                                   
                                     
                                       jω 
                                        
                                       
                                           
                                       
                                        
                                       C 
                                     
                                     + 
                                     
                                       1 
                                       R 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             1 
                             / 
                             
                               ( 
                               
                                 1 
                                 + 
                                 
                                   jω 
                                    
                                   
                                       
                                   
                                    
                                   
                                     L 
                                      
                                     
                                       ( 
                                       
                                         
                                           jω 
                                            
                                           
                                               
                                           
                                            
                                           C 
                                         
                                         + 
                                         
                                           1 
                                           R 
                                         
                                       
                                       ) 
                                     
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             1 
                             / 
                             
                               ( 
                               
                                 1 
                                 - 
                                 
                                   
                                     ω 
                                     2 
                                   
                                    
                                   LC 
                                 
                                 + 
                                 
                                   j 
                                    
                                   
                                     
                                       ω 
                                        
                                       
                                           
                                       
                                        
                                       L 
                                     
                                     R 
                                   
                                 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     
                       Formula 
                        
                       
                           
                       
                        
                       6 
                     
                     ) 
                   
                 
               
               
                 
                   
                     
                       G 
                       · 
                       β 
                     
                     = 
                     
                       G 
                       / 
                       
                         ( 
                         
                           1 
                           - 
                           
                             
                               ω 
                               2 
                             
                              
                             LC 
                           
                           + 
                           
                             j 
                              
                             
                               
                                 ω 
                                  
                                 
                                     
                                 
                                  
                                 L 
                               
                               R 
                             
                           
                         
                         ) 
                       
                     
                   
                 
                 
                   
                     ( 
                     
                       Formula 
                        
                       
                           
                       
                        
                       7 
                     
                     ) 
                   
                 
               
             
           
         
       
     
       Hereat, the Nyquist locus of the loop gain G.beta. is illustrated as shown in FIG. 10. The Nyquist locus doesn&#39;t enclose the point (1, j0) inside in the range of G less than +1. Therefore, this variable inductance LC resonant circuit is stable. 
       [0044]    Moreover, this variable inductance LC resonant circuit is possible to cover a wide frequency range even with low applied voltage. This can be proved by using an embodiment with a gain range, 
         [0000]      0 ≦G&lt;+ 1, 
         [0000]    which is easy to realize by an amplifier. In  FIG. 11 , a symbol  111  indicates a coil with inductance L, a symbol  112  indicates a capacitor with capacitance C, a symbol  113  indicates a pre-amplifier with a gain of +1 obtained by combining with a transistor  115 , a symbol  114  indicates a post-amplifier with a gain +1 by combining with a transistor  116 , symbols  117  and  118  indicate a current mirror transistor respectively, symbols  119  and  120  indicate a pair of differential transistors, symbol  121  indicates a buffer transistor, symbols  122  and  123  indicate constant current source respectively, symbols  124  and  125  indicate resistors determining the gain, symbols  126  and  127  indicate bias resistances, a symbol  128  indicates a coupling condenser, and a symbol  129  indicates an input terminal for inputting gain control signal. 
         [0045]      FIG. 12  and  FIG. 13  show an embodiment of the pre-amplifier and post-amplifier respectively. In these configuration, since the input bias for the pre-amplifier is provided from the post-amplifier via the coil, level shift circuit is configured with diodes. 
         [0046]    In  FIG. 11 , setting the resistances of the two resistors  122 ,  123  equal, it is possible to change the gain of the variable gain amplifier depending on the control signal input to the terminal  127 , which enables to change the resonant frequency from omega.sub. 0  to zero. This is explained with referencing to  FIG. 11  and following formulae. In  FIG. 11 , since the signal input to+terminal of the pre-amplifier appears at the emitter of the transistor  115 , denoting the resistance of the resistors  122 ,  123  R, following relations hold. 
         [0000]    
       
         
           
             
               
                 
                   
                     i 
                     0 
                   
                   = 
                   
                     
                       v 
                       i 
                     
                     R 
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     8 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     i 
                     0 
                   
                   = 
                   
                     
                       i 
                       1 
                     
                     + 
                     
                       i 
                       2 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     9 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     
                       
                         i 
                         1 
                       
                       
                         i 
                         2 
                       
                     
                     = 
                     
                        
                       x 
                     
                   
                    
                   
                     
 
                   
                    
                   
                     Here 
                     , 
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     10 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     x 
                     = 
                     
                       
                         v 
                         id 
                       
                       
                         v 
                         T 
                       
                     
                   
                   , 
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     11 
                   
                   ) 
                 
               
             
           
         
       
     
         [0000]    vid indicates gain control voltage, v T  indicates thermal voltage of the device, usually  26  mV. 
         [0047]    Since the relation of formula (12) holds, the gain G is expressed by formula (13), 
         [0000]    
       
         
           
               
             
               
                 
                   
                     
                       
                         i 
                         1 
                       
                       = 
                       
                         
                           1 
                           
                             1 
                             + 
                             
                                
                               
                                 - 
                                 x 
                               
                             
                           
                         
                         · 
                         
                           i 
                           0 
                         
                       
                     
                     , 
                   
                 
                 
                   
                     ( 
                     
                       Formula 
                        
                       
                           
                       
                        
                       12 
                     
                     ) 
                   
                 
               
               
                 
                   
                     
                       
                         
                           
                             G 
                             = 
                             
                               
                                 v 
                                 0 
                               
                               
                                 v 
                                 i 
                               
                             
                           
                         
                       
                       
                         
                           
                             = 
                             
                               
                                 ( 
                                 
                                   
                                     i 
                                     1 
                                   
                                   · 
                                   R 
                                 
                                 ) 
                               
                               / 
                               
                                 ( 
                                 
                                   
                                     i 
                                     0 
                                   
                                   · 
                                   R 
                                 
                                 ) 
                               
                             
                           
                         
                       
                       
                         
                           
                             = 
                             
                               
                                 i 
                                 1 
                               
                               / 
                               
                                 i 
                                 0 
                               
                             
                           
                         
                       
                       
                         
                           
                             = 
                             
                               1 
                               / 
                               
                                 ( 
                                 
                                   1 
                                   + 
                                   
                                      
                                     
                                       - 
                                       x 
                                     
                                   
                                 
                                 ) 
                               
                             
                           
                         
                       
                     
                     , 
                   
                 
                 
                   
                     ( 
                     
                       Formula 
                        
                       
                           
                       
                        
                       13 
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0000]    and then the relation of formula (14) holds. 
         [0000]    
       
         
           
               
             
               
                 
                   
                     
                       
                         
                           
                             ω 
                             r 
                           
                           = 
                           
                             
                               ω 
                               0 
                             
                              
                             
                               
                                 1 
                                 - 
                                 G 
                               
                             
                           
                         
                       
                     
                     
                       
                         
                           = 
                           
                             
                               ω 
                               0 
                             
                             / 
                             
                               
                                 1 
                                 + 
                                 
                                    
                                   x 
                                 
                               
                             
                           
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     
                       Formula 
                        
                       
                           
                       
                        
                       14 
                     
                     ) 
                   
                 
               
             
           
         
       
     
       The calculated value of .omega.sub.r/.omega.sub. 0  is shown in FIG. 14. In a range of x shown in FIG. 14, since the following relation, 
       [0048]    
       
         
           
             
               
                 
                   
                     1 
                     + 
                     
                        
                       
                         + 
                         7 
                       
                     
                   
                 
                 
                   
                     1 
                     + 
                     
                        
                       
                         - 
                         3 
                       
                     
                   
                 
               
               ≅ 
               32 
             
             , 
           
         
       
     
         [0000]    holds, it is possible to cover the frequency range from 150 kHz in LW band to 4.8 MHz in SW band. 
       Furthermore, performing the calculation of variation ratio with more wider range, 
       [0049]      −10≦×≦10   (Formula 15), 
         [0000]    the relation expressed by formula (16) holds, therefore, it is possible to cover the frequency range from 150 kHz in LW band to 22.2 MHz in SW band with control voltage ranging from −260 to +260 mV. 
         [0000]    
       
         
           
               
             
               
                 
                   
                     
                       
                         
                           
                             
                               
                                 1 
                                 + 
                                 
                                    
                                   
                                     + 
                                     10 
                                   
                                 
                               
                             
                             
                               
                                 1 
                                 + 
                                 
                                    
                                   
                                     - 
                                     10 
                                   
                                 
                               
                             
                           
                           ≅ 
                             
                            
                           
                             
                                
                               10 
                             
                           
                         
                       
                     
                     
                       
                         
                           ≅ 
                             
                            
                           148 
                         
                       
                     
                   
                 
                 
                   
                     ( 
                     
                       Formula 
                        
                       
                           
                       
                        
                       16 
                     
                     ) 
                   
                 
               
             
           
         
       
     
         [0050]      FIG. 15  shows an embodiment of a pre-amplifier whose bias is set independently, where a symbol  151  indicates the same amplifier as the variable gain amplifier shown in the broken line box in  FIG. 11 , a symbol  152  is a coupling condenser, a symbol  153  indicates a coil, a symbol  154  indicates a loss resistance associated with coil, a symbol  155  indicates a condenser included in the resonant circuit, a symbol  156  indicates a bias resistance, and a symbol  157  indicates a DC power source. In this configuration, the impedance of the serially connected coupling condenser  152  and coil  153  is inductive in the operation frequency range. However, since the input terminal and output terminal of the amplifier  151  are electrically shorted at the serial resonance, the resistance  154  is necessary to avoid the electrical short. The quality factor Qo of the resonant circuit deteriorates in the lower bias resistance  156  regime under the unload condition, and the bias voltage becomes depending on the base current of the transistor in the higher bias resistance regime. However, when the deterioration of the unload quality factor Qo is allowable, there is a big advantage that the virtual inductance L′ is variable from zero to infinity by merely changing the gain of the amplifier  151  from zero to +1. 
         [0051]    In addition, a conventional parallel tuning circuit comprising variable capacitors and fixed inductors has disadvantage that bandwidth becomes wider as frequency higher, narrower as frequency lower. To the contrary, the tuning circuit of the present invention comprising fixed capacitors and variable inductors has advantage that bandwidth is almost constant through the whole frequency band. In  FIG. 8 , a symbol  81  indicates a coil with inductance L′, a symbol  82  indicates a condenser with capacitance C, and a symbol  83  indicates a load resistor with resistance R connected the tuning circuit. Denoting the quality factor of the tuning circuit by Q, −3 dB down angular frequency bandwidth by BW, and a tuning angular frequency by .omega.sub.T, since the relation expressed by the formula (17) holds, 
         [0000]    
       
         
           
             
               
                 
                   
                     Q 
                     = 
                     
                       
                         R 
                         
                           
                             ω 
                             T 
                           
                            
                           
                             L 
                             ′ 
                           
                         
                       
                       = 
                       
                         
                           
                             ω 
                             T 
                           
                            
                           CR 
                         
                         = 
                         
                           
                             ω 
                             T 
                           
                           BW 
                         
                       
                     
                   
                   , 
                 
               
               
                 
                   
                     ( 
                     
                       Formula 
                        
                       
                           
                       
                        
                       17 
                     
                     ) 
                   
                   , 
                 
               
             
           
         
       
     
         [0000]    the relation expressed by the formula (18) holds. 
         [0000]    
       
         
           
             
               
                 
                   BW 
                   = 
                   
                     
                       
                         
                           ω 
                           T 
                           2 
                         
                          
                         
                           L 
                           ′ 
                         
                       
                       R 
                     
                     = 
                     
                       1 
                       CR 
                     
                   
                 
               
               
                 
                   ( 
                   
                     Formula 
                      
                     
                         
                     
                      
                     18 
                   
                   ) 
                 
               
             
           
         
       
     
         [0052]    As can be seen from the formula (18), although, regarding the tuning circuit of the prior art comprising variable capacitors and fixed inductors, the bandwidth increases with proportional to square of the resonant angular frequency, regarding the parallel resonant tuning circuit comprising the virtual variable inductor and fixed capacitor, the bandwidth is almost constant independent from the resonant angular frequency. This fact is very important for the radio receiver, because the capability of undesired signal rejection is invariant with respect to the every radio frequency. 
         [0053]    Regarding the relation between the frequency alignment and the transmitter power of the AM radio service in the world metropolitan, the transmitter power is generally higher for the lower frequency stations and lower for the higher frequency stations. However, since the bandwidth of the tuning circuit with variable condensers of the prior art increases at the higher frequency band, it is not possible to adequately reduce the undesired radio wave with high transmitter power in low frequency range. The tuning circuit with the variable inductance LC resonant circuit of the present invention has a big advantage regarding the point. 
         [0054]    Furthermore, a tap coupling or secondary is often necessary for the LC tuning circuit. In  FIG. 16 , such embodiment is illustrated. Since the variable inductance resonant circuit can provide bias voltage from the output of the post-amplifier  119  of the variable gain amplifier, the output can be directly connected to a collector of the transistor. 
         [0055]    Regarding the variable gain amplifier used in the variable inductance LC resonant circuit, in case that the input impedance of the pre-amplifier is not enough high compared to that of the condenser, the condenser is equivalent to that connected with the resistor in parallel, and in case that the output impedance of the post-amplifier is not low enough compared to that of the impedance of the coil, the coil is equivalent to that connected with the resistor in serial, and then the unload quality factor Qo of the resonant circuit is dumped, which results in the obstacle for the improvement of the sensitivity and selectivity. Therefore, it is desirable to use a negative feedback amplifier and the like. 
         [0056]    Large non-linearity existing in the gain of the variable gain amplifier used in this resonant circuit, modulation distortion occurs in the tuning circuit under the overload caused by the receiver input. Therefore, it is necessary to use a variable gain amplifier with good linearity. In the embodiment shown in  FIG. 11 , the linearity is improved, since the variable gain amplifier is adopted which forms negative feedback loop including the amplifier. 
         [0057]      FIG. 17  shows an embodiment in which the variable inductance LC resonant circuit is used in the oscillator. In  FIG. 17 , a symbol  171  indicates the variable inductance LC resonant circuit of the present invention shown in  FIG. 11 , a symbol  172  indicates a differential amplifier. The oscillator is configured by the feedback of the output of the pre-amplifier of the variable inductance LC resonant circuit  171  to the differential amplifier  172 . 
         [0058]    Furthermore, the pre-amplifier of the variable gain amplifier used in the variable inductance LC resonant circuit of the present invention has an advantage that the pre-amplifier can also be available as a RF amplifier with an AGC function.  FIG. 18  shows the embodiment. 
         [0059]    Moreover, the variable gain amplifier used in the variable inductance LC resonant circuit of the present invention has an advantage that it can also be available as a RF mixer.  FIG. 19  shows the embodiment. 
         [0060]    Providing a tuning circuit at the antenna stage, the desired signal can be separated from the noise or undesired signal, and then the interference can be avoided which is caused by the overload of the RF stage. Moreover, it is possible to omit the choke coil  32  shown in  FIG. 3 , which is necessary in the prior art to reduce the hum comes from the high voltage transmission line. 
         [0061]    In addition, since the tuning circuit used in the resonant circuit of the present invention has an advantage of being able to vary the tuning frequency with keeping the bandwidth constant, the tuning circuit has a character that the capability of the undesired signal rejection can be kept uniform in the whole frequency band compared with that of the prior art using the variable capacitance diodes. 
         [0062]    Although FETs with good linearity are additionally necessary for the RF amplifier of the prior art, however, since the amplifier with AGC function sharing the pre-amplifier of the variable inductance LC resonant circuit of the present invention adopts negative feedback, the amplifier with AGC function has good linearity and causes no modulation distortion for the strong undesired signals. 
         [0063]    Also regarding the mixer, the RF mixer of negative feedback type sharing the pre-amplifier of the variable inductance LC resonant circuit of the present invention has good linearity and causes no modulation distortion for the strong undesired signals. 
         [0064]    By adopting the variable inductance LC resonant circuit of the present invention, since a variable frequency tuning circuit can be configured by using the same variable gain amplifier in the IC tip, it is possible to omit variable capacitance diodes necessary to the prior art, a FET dedicated to the RF amplifier, the choke coil with large inductance for reducing the hum from the high voltage transmission line, and the like, and then expect to reduce the production cost. 
         [0065]      FIG. 5  shows an embodiment of the resonant circuit of the present invention. 
         [0066]      FIG. 11  shows an embodiment of the variable gain amplifier used in the resonant circuit of the present invention. 
         [0067]      FIG. 15  shows the other embodiment of the variable inductance LC resonant circuit of the present invention. 
         [0068]      FIG. 16  shows an embodiment of the variable inductance LC resonant circuit adopting the tap coupling and secondary coupling of the present invention. 
         [0069]      FIG. 17  shows an embodiment of the differential oscillator using the resonant circuit of the present invention. 
         [0070]      FIG. 18  shows an embodiment of sharing the pre-amplifier of the variable inductance LC resonant circuit of the present invention with a RF amplifier having AGC function. A symbol  181  indicates a transistor, and a symbol  182  indicates differential transistors for controlling the gain depending on the AGC signal. 
         [0071]      FIG. 19  shows an embodiment of sharing the pre-amplifier of the variable inductance LC resonant circuit of the present invention with a RF mixer. A symbol  191  indicates a transistor, a symbol  192  indicates a couple of differential transistors switching according to the local oscillator signal, and a symbol  193  indicates a LC coupling circuit. 
         [0072]      FIG. 21  shows a radio receiver using the variable inductance LC resonant circuit of the present invention, comparing with that of the prior art shown in  FIG. 20 . 
         [0073]    In  FIG. 20 , a symbol  11  indicates electromotive force generated in the antenna, a symbol  12  indicates antenna resistance, a symbol  13  indicates antenna capacitance, a symbol  14  indicates cable capacitance, a symbol  32  indicates a choke coil for reducing the hum from the high voltage transmission line, a symbol  206  indicates a RF amplifier, symbols  207 ,  209  indicate a tuning circuit with a variable capacitance diode respectively, a symbol  210  indicates a RF mixer, a symbol  211  indicates a local signal generator using variable capacitance diodes, a symbol  212  indicates an IF filter, a symbol  213  indicates an IF amplifier, a symbol  214  indicates a detector, a symbol  215  indicates an audio amplifier, a symbol  216  indicates a speaker, a symbol  217  a signal generator for AGC, a symbol  218  indicates a signal line for transmitting AGC signal, a symbol  219  is a PLL circuit, a symbol  220  indicates a quartz oscillator for generating reference signal, a symbol  221  indicates a signal line for transmitting the output of the local signal generator, and a symbol  222  indicates signal lines for transmitting the voltage signal for controlling the variable capacitance diodes of the resonant circuits of both tuning circuit and the local signal generator. 
         [0074]    In  FIG. 21 , symbols  205 ,  207 ,  209  indicate the tuning circuit using the variable inductance LC resonant circuit of the present invention, a symbol  206 ,  208  indicate a RF amplifier respectively, a symbol  210  indicates a RF mixer, and a symbol  222  indicates signal lines for transmitting the voltage signal for controlling the frequency of the resonant circuits of both tuning circuit and the local signal generator. 
         [0075]    The four portions surrounded by the broken line shown in  FIG. 21  indicate an antenna equivalent circuit  11 ,  12 ,  13 ,  14 , two RF amplifiers  206 ,  208  with the tuning circuit  205 ,  207  shown in  FIG. 18  each, and a RF mixer  210  with a tuning circuit  209  shown in  FIG. 19 , respectively.