Patent Publication Number: US-7596361-B2

Title: Low noise amplification circuit

Description:
BACKGROUND OF THE INVENTION 
   1. Field of the Invention 
   The present invention relates to a low noise amplification circuit which amplifies high-frequency and weak signals received by means of antennas, and especially relates to a low noise amplification circuit which comprises at least one filter coupled to the input terminal of a low noise amplifier to remove undesired frequency components. 
   2. Description of the Related Art 
   Generally, wireless instruments, such as cellular phones or GPS devices, include at least one receiving device with a low noise amplifier (LNA) which amplifies signals within predetermined frequency bands received by means of antennas. However, the antennas receive not only signals within a desired frequency band, but also signals with undesired frequency components near the desired frequency band. For instance, when another wireless instrument is placed close to the receiving device, and transmits or receives radio waves with so large electric field, the undesired frequency components might be received with so large level compared to the signals within the desired frequency bands. As a result, it is likely that the LNA is saturated with the undesired frequency components such that the LNA cannot amplify the signals within the desired frequency bands. 
   In order to prevent the problem described above, there is proposed a receiving device in which undesired components are removed by at least one filter coupled to the input terminal of the LNA (ex. JP07-058657A, JP2002-164803A). JP07-058657A discloses a receiving device in which undesired components are removed by a band-pass filter coupled to a front end of the LNA. JP2002-164803A discloses a receiving device in which specific frequency bands close to desired frequency bands are removed by a trap circuit arranged between the antenna and the LNA as a band-stop filter. 
   In the conventional receiving device as described above, the filter coupled to the input terminal of the LNA yields an insertion loss for the signals within the desired frequency band. In general, since a noise figure of a whole circuit is roughly determined due to a noise figure of the first stage of the circuit, the loss yielded before the LNA significantly affects the noise figure of a whole circuit. Accordingly, when a filter is arranged at the front end of the LNA , the insertion loss of the filter directly leads to the deterioration of the noise figure of the whole circuit. When the noise figure is deteriorated due to the filter arrangement, a receiving quality is deteriorated in a receiving instrument for, in particular, the digital modulation system. More specifically, the  FIG. 13  shows that the transmitting quality or the transmitting speed is degraded because a bit error rate is significantly deteriorated along with a signal-noise ratio in various digital transmitting systems. When the circuit is applied to a receiving instrument for satellite signals, the communication area might scale down due to the degradation of minimum receiver sensitivity. To solve the problem, it is possible to employ a high performance LNA with excellent noise characteristic, however, it is inevitable that the cost must run much high. When a high performance filter is employed in order to reduce the insertion loss of the filter, a similar problem occurs. 
   BRIEF SUMMARY OF THE INVENTION 
   An object of the present invention is to solve the problem as described above. More specifically, the present invention intends to make it possible to produce a low noise amplification circuit with excellent noise characteristic in which the deterioration of noise figure due to the insertion loss of the filter is reduced while the undesired frequency components are removed by the filter arranged at the input side of the LNA. 
   In a first aspect of the present invention, a low noise amplification circuit which amplifies signals by a predetermined gain, comprises at least a low noise amplifier including at least an amplifying element and a matching input circuit coupled to an input terminal of the amplifying element, and a filter coupled to an input terminal of the low noise amplifier, wherein when gamma.sub.s represents a reflection factor, impedance conversion for the gamma.sub.s to be set at a desired value is made entirely or in part in such manner that an output impedance of the filter at the value is set to be different from that of characteristic impedance in a case that signals flow from the input terminal of the amplifying element to the output terminal of the matching input circuit. 
   According to this aspect of the present invention, the input signals to the low noise amplification circuit are within desired frequency bands in the result of removing undesired frequency components by means of the filter, input to the amplifying element through the matching input circuit, and are amplified at a predetermined gain. In this case, the output impedance of the filter is set to a value different from the characteristic impedance. For example, a field-effect transistor (FET) or a bipolar transistor are used as the amplifying element, the noise figure is determined depending on the amplifying element. The matching input circuit is used in order to convert the impedance from the output impedance of the filter to the input impedance of the amplifying element, and can be designed by either a lumped-constant circuit or a distributed constant circuit. 
   In another aspect of the present invention, a following formula is satisfied:
 
 L .sub. i&lt;L .sub. f+N .sub. m− 10 Log(1−|gamma.sub. s|   2 )
 
where L.sub.f (dB) represents an insertion loss of the filter in a case that both of the input and output impedances are set to be the characteristic impedance, L.sub.i (dB) represents an insertion loss of a circuit consisting of the matching input circuit and the filter of which output impedance is different from the characteristic impedance, N.sub.m (dB) represents a degradation amount of noise figure of the matching input circuit.
 
   It is necessary to set the reflection factor of the matching input circuit in order to optimize the noise figure of the low noise amplification circuit so that the above formula is met. In this case, a noise-optimized signal-source reflection factor gamma.sub.opt for optimizing the noise figure is determined depending on the kind of the amplifying element and the use conditions, and therefore the reflection factor at the output terminal of the matching input circuit is set to the value close to the gamma.sub.opt. As a result, the insertion loss of the input signals and the deterioration amount of the noise figure is concerned appropriately. Like this, an optimally designed low noise amplification circuit has an excellent noise characteristic along with a necessary gain compared to the conventional design method based upon the characteristic impedance. 
   In another aspect of the present invention, the L.sub.f (dB), the L.sub.i (dB), the N.sub.m (dB) and the gamma.sub.s satisfy a following formula:
 
 L .sub. i&lt;L .sub. f+N .sub. m− 10 Log(1−|gamma.sub. s|   2 )−0.1
 
   In another aspect of the present invention, the L.sub.f (dB), the L.sub.i (dB) and the gamma.sub.s satisfy a following formula:
 
 L .sub. i&lt;L .sub. f− 10 Log(1−|gamma.sub. s|   2 )
 
   These aspects of the present invention make it possible to perform the above impedance conversion more accurately along with the above advantage of the present invention, and therefore to improve the more excellent noise characteristic. 
   In another aspect of the present invention, the gamma.sub.s is approximately equal to a gamma.sub.opt, which is a noise-optimized signal-source reflection factor of the amplifying element. 
   In another aspect of the present invention, the matching input circuit of the low noise amplification circuit consists of a reactance element. 
   According to the above aspect of the present invention, the low noise amplification circuit has a impedance conversion with a simple circuit made of such a reactance element as series inductances or parallel capacitance. 
   In another aspect of the present invention, the input signals are high-frequency signals received by means of an antenna. 
   According to the above aspect of the present invention, the low noise amplification circuit can amplify weak high-frequency signals received by means of an antenna with the optimum noise characteristic, and therefore can realize a receiving device with excellent receiving performances. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
     The above and other objects and features of the invention will appear more fully hereinafter from a consideration of the following description taken in connection with the accompanying drawing wherein one example is illustrated by way of example, in which; 
       FIG. 1  is a block diagram showing the main construction of a receiving device comprising a low noise amplification circuit according to an embodiment of the present invention; 
       FIG. 2  is a block diagram showing an internal construction of the LNA according to the embodiment of the present invention; 
       FIG. 3   a ,  FIG. 3   b  and  FIG. 3   c  show the conditions of impedance matching respectively in the filter, the matching input circuit and the amplifying element according to the present embodiments on a Smith charts; 
       FIG. 4   a  and  FIG. 4   b  show the characteristics of the filter designed as an embodiment according to the present invention,  FIG. 4   a  shows the frequency characteristics of the insertion loss, and  FIG. 4   b  shows the reflection factor at the output terminal; 
       FIG. 5   a  and  FIG. 5   b  show the characteristics of a filter with a conventional construction corresponding to the filter according to the present embodiment,  FIG. 5   a  shows the frequency characteristics of the insertion loss, and  FIG. 5   b  shows the reflection factor at the output terminal; 
       FIG. 6   a  and  FIG. 6   b  show the characteristics of the circuit part made of the filter and the matching input circuit coupled to the output terminal of the filter according to the embodiment,  FIG. 6   a  shows the frequency characteristics of the insertion loss, and  FIG. 6   b  shows the reflection factor at the output terminal; 
       FIG. 7   a  and  FIG. 7   b  show the concept of impedance transformation in order to change the reflection factor gammma.sub.mid to gammma.sub.opt in a Smith chart, and  FIG. 7   a  shows the impedance transformation of a construction of the embodiment, and  FIG. 7   b  shows the impedance transformation of a conventional construction; 
       FIG. 8   a  and  FIG. 8   b  show constructional examples of the matching input circuit in order to realize the impedance transformation in  FIG. 7   a  and  FIG. 7   b ,  FIG. 8   a  shows a constructional example of the embodiment, and  FIG. 8   b  shows a conventional constructional example; 
       FIG. 9   a  and  FIG. 9   b  show the characteristics of the filter and the LNA in the embodiment, and show the frequency characteristics of gain and noise figure respectively; 
       FIG. 10   a  and  FIG. 10   b  show the characteristics of the filter and the LNA in a conventional example corresponding to the embodiment, and show the frequency characteristics of gain and noise figure respectively; 
       FIG. 11   a  and  FIG. 11   b  show the characteristics of the filter designed as another embodiment according to the present invention, and show respectively the frequency characteristics of the insertion loss and the reflection factor at the output terminal; 
       FIG. 12   a  and  FIG. 12   b  show the characteristics of the filter and the LNA in another embodiment, and show the frequency characteristics of gain and noise figure respectively; and 
       FIG. 13  shows deteriorations of bit error rates along with deteriorations of signal-noise ratios in various digital modulation methods. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
   A preferred embodiment of the present invention is described below with reference to the figures.  FIG. 1  is a block diagram showing a receiving device comprising a low noise amplification circuit according to an embodiment of the present invention. The receiving device in  FIG. 1  includes an antenna  11  to receive electric waves, the filter  12  to remove undesired frequency components, the LNA  13  to amplify received signals at a predetermined gain, which are connected in sequence, and a high-frequency circuit thereafter in which the received signals to be amplified with low-noise are processed. The low noise circuit according to the present invention comprises the filter  12  and the LNA  13 . 
   A GPS receiving device to receive electric waves from GPS satellites is described as an example of the receiving device in  FIG. 1 . In this case, the frequency characteristic of the antenna  11  is designed so that signals with a desired frequency of 1.57 GHz in a frequency band for GPS will be received. The output impedance of the antenna  11  is set to be the characteristic impedance, which is 50 Ω in general. That is, it is possible to use an antenna matching circuit connected at the output terminal of the antenna  11 , not shown, for impedance matching for example. 
   The filter  12  has a frequency characteristic to remove undesired frequency components along with passing signals within desired frequency band. Any of a band-pass filter, a band-stop filter, a low-pass filter and a high-pass filter can be used as the filter  12 . A band-pass filter is preferred when various kind of undesired waves exist around the desired frequency band. A band-stop filter is preferred when undesired waves with large power and specific frequencies exist close to the desired frequency band. For example, it is necessary to remove the frequency band of 0.9 to 1 GHz for cellular phones (PDC) in order to receive low noise GPS signals with a frequency of 1.57 GHz when the cellular phones are used close to GPS devices. 
   Received signals with weak power from which undesired frequency components are removed by means of the filter  12  are input to the LNA  13 .  FIG. 2  is a block diagram showing an internal construction of the LNA  13 . The LNA  13  includes the matching input circuit  21 , the amplifying element  22  and the matching output circuit  23  which are connected in sequence. In this configuration, such an element device as an FET which has an excellent noise characteristic in high frequency band is used as the amplifying element  22 , amplifies input signals at a predetermined gain. Next, the matching input  21  is a circuit for impedance matching between the filter  12  connected at the input terminal of the matching input circuit  21  and the amplifying element  22 . The matching output circuit  23  is a circuit for impedance matching between the amplifying element  22  and a high frequency circuit connected at the output terminal of the matching circuit  23 . 
   The high frequency circuit to which output signals from the LNA  13  are input may be formed in various manner depending on functions required for the receiving device. For example, the high frequency circuit may include a circuit to combine filters and amplifiers in multiple stages, or demodulation circuit to demodulate received signals, and the like. 
   In embodiments of the present invention, the impedance matching is effected at the respective connection points in the filter  12 , the matching input circuit  21  and the amplifying element  22  which are connected in sequence.  FIG. 3   a  to  FIG. 3   c  show the conditions of the respective impedance matching in the filter, the matching input circuit and the amplifying element according to the present embodiments by use of Smith charts. 
   At first, the input impedance of the filter  12  is set to be roughly the characteristic impedance Z.sub.0, which is in usual 50 Ω, since the antenna  11  or the matching circuit thereof is connected to the input side of the filter  12 . The Smith charts in  FIG. 3   a  to  FIG. 3   c  show the respective reflection factors to matching impedances with the center points as the basis, which correspond to the characteristic impedance Z.sub.0. As shown in  FIG. 3   a , since the input impedance of the filter  12  is set so as to match with the characteristic impedance Z.sub.0, the reflection factor at the front end of the filter  12  is described as the gammma.sub.0 at the center of the Smith chart which means no reflection. Here, respective reflection factors are expressed by means of complex numbers with amplitude components and phase components, or real parts and imaginary parts. 
   Meanwhile, as shown in  FIG. 3   b , as the output impedance of the filter  12  is set so as to match with a specific impedance Z.sub.mid different from the characteristic impedance Z.sub.0, the reflection factor at the back-end of the filter  12  is expressed by means of the gammma.sub.mid corresponding to the distance between the center point and the position of the impedance Z.sub.mid on the Smith chart. In the same way, the input impedance of the matching input circuit  21  is set to Z.sub.mid* (“*” shows complex conjugate.) so as to match with the above impedance Z.sub.mid. In this case, the reflection factor gammma.sub.mid may be set to be various values under the condition that the output impedance of the filter  12  matches with the input impedance of the matching input circuit  21  so as not to occur reflections due to mismatching. 
   Furthermore, the noise characteristic of the amplifying element  22  is determined depending on the input impedance thereof, and therefore it is necessary to set the reflection factor at the front end of the amplifying element  22  to be the noise-optimized signal-source reflection factor gamma.sub.opt in order to optimize the noise characteristic. As shown in  FIG. 3   c , the noise-optimized signal-source reflection factor gamma.sub.opt is determined depending on the distance between the center point and the position corresponding to the predetermined impedance Z.sub.opt. Accordingly, as shown in  FIG. 2 , the output impedance of the matching input circuit  21  is set so as to optimize the noise characteristic of the amplifying element  22 , and it is necessary to accord the reflection factor at the back-end of the matching input circuit with the noise-optimized signal-source reflection factor gamma.sub.opt along with this. 
   Here, the matching output circuit may be designed depending on the output impedance of the amplifying element  22  and the impedances of the circuit parts used thereafter. In this case, it is preferred to determine the design condition for the matching output circuit  23  in consideration of necessary gain of the LNA and stability of operation. 
   In the present embodiment, it is possible to simplify the matching input circuit  21  where the above described LNA  13  is employed. More specifically, when the reflection factors gammma.sub.0s at both of the front end and back-end of the filter  12  are set to be zero where the input impedance and output impedance of the filter  12  are matched with the characteristic impedance Z.sub.0 as shown in the conventional construction, it is necessary to adjust the matching input circuit  21  to transform the impedance to the relatively far position on a Smith chart from the reflection factor gammma.sub.0 to the noise-optimized signal-source reflection factor gamma.sub.opt. On the contrary, in the present embodiment, it is possible to set the reflection factor at the back-end of the filter  12  to be the reflection factor gammma.sub.mid to transform the impedance to relatively near position on a Smith chart from the reflection factor gammma.sub.mid to the noise-optimized signal-source reflection factor gamma.sub.opt, and moreover it is possible to obtain the characteristics of the LNA  13  equal to or more than a conventional LNA. 
   Next, a specific design example of the present embodiment is described below. The operating conditions as described below are for a GPS receiving device. Here, there is used a band-stop filter to remove frequency bands for cellular phone (PDC) as the filter  12 , there is used an amplifier which can amplify GPS signals with a GPS frequency as the LNA  13 , and there is used a GaAs FET as the amplifying element  22 , respectively. However, as described below, conventional examples with such constituent elements as the above constituent elements are also described in order to compare with the specific design example of the present embodiment. 
   The noise-optimized signal-source reflection factor gamma.sub.opt of the amplifying element  22  has amplitude of 0.582 and a phase angle of 27.004 degree corresponding to the above operating condition. 
   The filter  12  has the characteristics as shown in  FIG. 4   a  and  FIG. 4   b .  FIG. 4   a  shows the frequency characteristics of the insertion loss of the filter  12  based upon the design according to the present invention. As shown in  FIG. 4   a , the insertion loss of the filter  12 , which is shown as an S-parameter S 21 , changes in the frequency range of 0.4 to 2.6 GHz. It is shown that the filter  12  passes signals within the frequency band for GPS with an insertion loss of about 1 dB, and at the same time, an attenuation amount for the GPS frequency band is about 58 dB. 
     FIG. 4   b  shows the frequency characteristics of the reflection factor at the output terminal of the filter  12 . As shown in  FIG. 4   b , the reflection factor (the impedance) at the output terminal of the filter  12 , which is shown as a S-parameter S 22 , changes along the path on the Smith chart corresponding to frequency changes. And in the frequency band for PDC, the reflection factor gamma.sub.mid has roughly amplitude of 0.393 and a phase angle of 26.163 degree. 
     FIG. 5   a  and  FIG. 5   b  show the characteristics of a filter with a conventional construction corresponding to the above filter  12 .  FIG. 5   a  and  FIG. 5   b  show the characteristics of the filter whose input and output impedances match with the characteristic impedance based upon the similar condition to that in  FIG. 4   a  and  FIG. 4   b . The frequency characteristic of insertion loss as shown in  FIG. 5   a  is similar to that as shown in  FIG. 4   a , but the frequency characteristic of reflection factor as shown in  FIG. 5   b  is entirely different from that as shown in  FIG. 4   b . The filter with the conventional construction has an output impedance matching with the characteristic impedance Z.sub.0, and therefore the reflection factor at the output terminal of the filter is close to zero. On the contrary, the filter  12  of the present embodiment has an output impedance meaningly misaligned from the characteristic impedance Z.sub.0, and the reflection factor gammma.sub.mid in this case has a predetermined value quite more than zero. And the reflection factor gammma.sub.mid has a value less the noise-optimized signal-source reflection factor gamma.sub.opt, that is, close to the center of a Smith chart. Therefore it is necessary to transform the input impedance of the amplifying element  22  from the gammma.sub.mid to the gammma.sub.opt. 
   The circuit part where the matching input circuit  21  is connected to the output terminal of the filter  12  has the characteristics as shown in  FIG. 6   a  and  FIG. 6   b .  FIG. 6   a  shows the frequency characteristics of the insertion loss in the circuit part comprising the filter  21  and the matching input circuit  21 . The characteristic as shown in  FIG. 6   a  is roughly similar to that as shown in  FIG. 4   a .  FIG. 6   b  shows the characteristic of the reflection factor at the output terminal of the circuit part comprising the filter  21  and the matching input circuit  21 . The characteristic as shown in  FIG. 6   b  is different from that as shown in  FIG. 4   b , and the reflection factor gamma.sub.s has amplitude of about 0.574 and a phase angle of about 28.402 degree in the frequency band for GPS. This reflection factor gamma.sub.s is set to a value relatively close to or roughly equal to the noise-optimized signal-source reflection factor gamma.sub.opt. 
     FIG. 7   a  and  FIG. 7   b  show the concept of impedance transformation in order to change the reflection factor gamma.sub.mid to gamma.sub.opt in a Smith chart. The following description is based upon the gamma.sub.s equal to the gamma.sub.opt as described above.  FIG. 7   a  shows the impedance transform from the gamma.sub.mid to the gamma.sub.opt in the construction of the embodiment, and  FIG. 7   b  shows the impedance transformation from the gamma.sub.0 to the gamma.sub.opt in the conventional construction for comparison. 
   In  FIG. 7   a , the reflection factor is transformed from the gamma.sub.0 corresponding to the characteristic impedance Z.sub.0, which is at the center of the Smith chart, to the gamma.sub.mid by means of the filter  12 . And the reflection factor is transformed from the gamma.sub.mid to the gamma.sub.opt by means of the matching input circuit connected to the filter  12 . While, in  FIG. 7   b , the reflection factor is directly transformed from the gamma.sub.0, which is at the center of the Smith chart, to the gamma.sub.opt by means of the matching input circuit  21 . 
   Meanwhile,  FIG. 8   a  and  FIG. 8   b  show examples of the matching input circuit  21  for the impedance transformation as shown in  FIG. 7   a  and  FIG. 7   b .  FIG. 8   a  is a example of the matching input circuit  21  according to the present embodiment, which is a construction using serial inductors. On the contrary,  FIG. 8   b  is a conventional example of the matching input circuit, which is a construction using parallel capacitors along with serial inductors. In this way, as there is reduced a change of the reflection factor on the Smith chart in the matching input circuit  21  according to the present embodiment, the construction of the matching input circuit  21  can be simplified compared to the conventional construction. Here, the matching input circuit  21  of the present embodiment can be made of parallel capacitors depending on settings of the reflection factor gamma.sub.mid, but can be made of at most one reactance element. 
   Next, there is described the noise figure characteristic of the LNA  13  according to the present embodiment. At first, when S-parameters of the stand-alone matching input circuit is illustrated as shown in the following formula (1), 
                   Matrix   ⁢           ⁢     S   .   sub   .   M       =     [             S   .   sub   .   M     ⁢           ⁢   11             S   .   sub   .   M     ⁢           ⁢   12                 S   .   sub   .   M     ⁢           ⁢   21             S   .   sub   .   M     ⁢           ⁢   22           ]             (   1   )               
the deterioration amount of noise figure N.sub.m (dB) of the matching input circuit  21  is illustrated as shown in the following formula (2).
 
                               N   .   sub   .   m               (   dB   )           =       -   10     ⁢     Log   ⁡     [                S   .   sub   .   M     ⁢           ⁢   21          2     /     (     1   -              S   .   sub   .   M     ⁢           ⁢   21          2       )       ]                     =         -   10     ⁢   Log   ⁢              S   .   sub   .   M     ⁢           ⁢   21          2       +     10   ⁢           ⁢     Log   ⁡     (     1   -              S   .   sub   .   M     ⁢           ⁢   21          2       )                         (   2   )               
And, the insertion loss of 50 ohms system L.sub.m is illustrated as shown in the following formula (3) by means of calculating from the above two formulas.
 
   
     
       
         
           
             
               
                 
                   
                     
                       
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   The above formula (3) shows that there is some difference between the deterioration amount of noise figure N.sub.m and the insertion loss L.sub.m by a loss improvement amount of the insertion loss due to the impedance matching at the back-end of the matching input circuit  21  in relation to the insertion loss of the matching input circuit. In this case, when the output impedance of the matching input circuit  21  in the construction of the present embodiment is equal to that in the construction of the conventional example, the noise figure will be improved by the loss improvement amount of 50 ohms system. 
   Based upon the above formula (3), the following formula (4) is introduced with use of the insertion loss L.sub.i of a circuit part, the reflection factor gamma.sub.s at the back-end of the circuit part and the insertion loss L.sub.f of the simple filter  12 . Here, the circuit part is constituted by the filter  12  and the matching input circuit  21 , and the input and output impedances of the filter  12  are set to the characteristic impedance.
 
 L .sub. i ( dB )&lt; L .sub. f+N .sub. m− 10 Log(1−|gamma.sub. s|   2 )  (4)
 
   The noise figure of a receiving device is kept good by means of determining the design conditions of the filter  12  and the LNA  13  so as to meet the above formula (4). 
   And, it is preferred to apply the following formulas (5) or (6) instead of the above formula (7) in order to improve the noise characteristics moreover.
 
 L .sub. i ( dB )&lt; L .sub. f+N .sub. m− 0.1−10 Log(1−|gamma.sub. s|   2 )  (5)
 
 L .sub. i ( dB )&lt; L .sub. f− 10 Log(1−|gamma.sub. s|   2 )  (6)
 
   Next, there is described the characteristics of the filter  12  and the LNA  13  integrated in the present embodiment.  FIG. 9   a  and  FIG. 9   b  show the characteristics of the filter  12  and the LNA  13  in the present embodiment, and  FIG. 10   a  and  FIG. 10   b  show the characteristics of the filter  12  and the LNA  13  in a conventional example for comparison.  FIG. 9   a  shows the gain-frequency characteristic of the whole of the filter  12  and the LNA  13 , and  FIG. 10   a  shows the similar characteristic of the conventional construction. In the frequency band for GPS among predetermined frequency bands, while the low noise amplification circuit according to the present embodiment had a gain of 15.744 dB, the noise amplification circuit with the conventional construction had a gain of 15.323 dB. 
   Next,  FIG. 9   b  shows the noise figure frequency characteristic of the whole of the filter  12  and the LNA  13 , and  FIG. 10   b  shows the similar characteristic of the conventional construction. In the frequency band for GPS among a frequency range of 1 to 2 GHz, while the low noise amplification circuit according to the present embodiment had noise figure of 1.104 dB, the noise amplification circuit with the conventional construction had noise figure of 1.275 dB. 
   And,  FIG. 6   a  and  FIG. 6   b  shows the insertion loss L.sub.i in the circuit part made of the filter  12  and the matching input circuit  21  was 2.268 dB. And the noise figure deterioration amount N.sub.i in a similar circuit is 0.548 dB. Meanwhile,  FIG. 5   a  and  FIG. 5   b  show that the insertion loss of the simple filter  12  in the 50 ohms system was 0.514 dB, and that the noise figure deterioration amount N.sub.m is 0.219 dB, and  FIG. 6   a  and  FIG. 6   b  show the reflection factor gamma.sub.s is 0.574. Therefore, the right-hand side of the formula (4) was calculated as shown in the following formula (7). 
                                 L   .   sub   .   f     +     N   .   sub   .   m     -               10   ⁢     log   ⁡     (     1   -            gamma   .   sub   .   s          2       )               =       ⁢     0.514   +   0.219   +                     ⁢     10   ⁢           ⁢     Log   ⁡     (     1   -     0.574             ⁢   2         )                     =       ⁢   2.469                 (   7   )               
The above L.sub.i of 2.268 dB is less than the calculation result of the right-hand side, and therefore the formula (4) was met. In such as GPS receiving device described as a specific embodiment, the F.sub.min is 0.5 to 0.7 dB, and the noise figure of the low noise amplifier is 1.0 to 1.5 dB, and therefore noise figure improvement of 0.1 dB also provides significant effect. In the construction of the present embodiment, the right-hand side of the formula (5) was calculated as shown in the following formula (8).
 
                                     L   .   sub   .   f     +     N   .   sub   .   m     -   0.1   -     ⁢                       10   ⁢     log   ⁡     (     1   -            gamma   .   sub   .   s          2       )               =       ⁢     0.514   ⁢           +           ⁢   0.129   -   0.1   +       ⁢                           ⁢     10   ⁢           ⁢     Log   ⁡     (     1   ⁢           -           ⁢     0.574             ⁢   2         )                     =       ⁢   2.369                 (   8   )               
The above L.sub.i of 2.268 dB is less than the calculation result of the right-hand side of the formula (5), and therefore the formula (5) is met. So it was shown to improve noise figure efficiently by use of the present embodiment. Sequentially, it was proved that the construction of the present embodiment can improve noise figure by about 0.18 dB without the deterioration of gain characteristics compared to the conventional construction.
 
   Next, there is described another embodiment according to the present invention. In the above embodiment, there was described the case that the reflection factor gamma.sub.mid was different from the noise-optimized signal-source reflection factor gamma.sub.opt. In this another embodiment, there is described the construction with the gamma.sub.mid equal to the gamma.sub.opt. Here, the construction and the operation of the filter  12  and the matching input circuit  21  is similar to those of the above embodiment, and the description thereof is omitted. 
     FIG. 11   a  and  FIG. 11   b  show the characteristics of the filter  12  in another embodiment.  FIG. 11   a  shows the insertion loss frequency characteristic of the filter  12 , and  FIG. 11   b  shows the frequency characteristic of the reflection factor at the back-end of the filter  12 . This filter  12  is a band-stop filter made of two series resonant circuits connected serially, and has an attenuation of about 54 dB within the frequency band for cellular phones (PDC). Furthermore, within the frequency band for GPS, there was obtained the gamma.sub.mid with amplitude of 0.574 and a phase angle of 26.077 degree, which is roughly equal to the gamma.sub.opt. 
     FIG. 12   a  and  FIG. 12   b  show the characteristics of the filter  12  and the matching input circuit  21  in the present another embodiment.  FIG. 12   a  shows a gain frequency characteristic of the whole of the filter  12  and the matching input circuit  21  in the present another embodiment,  FIG. 12   b  shows the characteristic of noise figure. As shown in  FIG. 12   a  and  FIG. 12   b , the present another embodiment had a gain of 15.52 dB and noise figure of 1.073 dB, and could improve the noise figure by 0.21 dB. 
   Here, in the present another embodiment, the circuit part made of the filter  12  and matching input circuit  21  had a insertion loss L.sub.i of 2.225 dB, and the noise figure deterioration amount N.sub.i of 0.496 dB. Therefore the right-hand side of the formula (6) was calculated as shown in the following formula (9), and the calculation result shows more improvement compared to the above embodiment.
 
 L .sub. f− 10 Log(1−|gamma.sub. s|   2 )=0.514+10 Log(1−0.574 2 )=2.250  (9)
 
   It is possible to apply the present invention as described above to various devices including low noise amplification circuits, which are made of the filter and the LNA, without limitation to the above constructions of the embodiments. And it is possible to apply the present invention in order to amplify not only the signals received by means of antennas, but also weak high-frequency signals with excellent noise characteristics. 
   According to the present invention, in the result that the filter to remove undesired frequency components and the matching input circuit necessary for impedance transformations are arranged at the front end of the amplifying element, and that respective reflection factors and impedances are designed so as to meet predetermined conditions, there is reduced the deterioration of the noise characteristics, which occurs due to insertion losses, and there is realized the noise characteristics more excellent compared to the conventional construction. In addition to that, as it is possible to make impedance transformations with use of simple constructions, it is possible to improve the noise characteristics with reduction of the number of parts and reduction of costs. 
   The present invention is not limited to the above described embodiments, and various variations and modifications may be possible without departing from the scope of the present invention. 
   This application is based on the Japanese Patent application No. 2005-157951 filed on May 30, 2005, entire content of which is expressly incorporated by reference herein.