Active bandpass filter

An active bandpass filter offers freely settable values of quality factor Q and peak gain. The active bandpass filter has a first, a second and a third transistor. The first transistor has a base connected to an input terminal of the filter via a first resistance element, a collector connected both to a constant voltage source via a second resistance element and to an output terminal of the filter and an emitter connected to a first constant current source. The second transistor has a base connected to the emitter of the first transistor via a third resistance element, a collector connected to the constant voltage source via a fourth resistance element and an emitter connected both to the base of the first transistor via a first capacitance element and to a second constant current source. The third transistor has a base connected to the collector of the second transistor, a collector connected to the constant voltage source and an emitter connected both to the base of the second transistor via a second capacitance element and to a third constant current source. Resistors can be used instead of the constant current sources.

BACKGROUND OF THE INVENTION 
The present invention relates to a bandpass filter which uses active 
elements, that is, to an active bandpass filter, and more particularly to 
an active bandpass filter with improved degree of freedom in setting 
quality factor Q and peak gain. 
FIG. 1 is a schematic circuit diagram an example of the configuration of a 
conventional bandpass filter. In this drawing, an input terminal 31 which 
accepts an input signal v.sub.i is connected to one end of a capacitor 32, 
which has a capacitance value of C.sub.31. The other end of the capacitor 
32 is connected to one end of a resistor 33 which has a resistance value 
of R.sub.31, and also to one end of a resistor 34 which has a resistance 
value of R.sub.32. The other end of the resistor 33 is grounded. The other 
end of the resistor 34 is grounded through a capacitor 35 which has a 
capacitance value of C.sub.32, and is also connected to an output terminal 
36 used to output an output signal v.sub.o. 
In a filter circuit such as described above, the transfer function G(b/a) 
is given by equation (1). 
##EQU1## 
The cutoff frequency .omega..sub.0 is expressed by equation (2). 
##EQU2## 
The quality factor Q and the peak gain H are expressed by equation (3) and 
equation (4), respectively. 
##EQU3## 
However, in a conventional bandpass filter, such as shown in FIG. 1, there 
is a shortcoming in that the quality factor Q cannot be set to a value of 
0.5 or higher. Another shortcoming is that it is not possible to have a 
peak gain H of 1 or higher. 
If the substitutions C.sub.31 nC.sub.32 and R.sub.31 =mR.sub.32 (n, m&gt;0) 
are made in equation (2), the cutoff frequency .omega..sub.0 is expressed 
as in equation (5), so that the quality factor Q is expressed as in 
equation (6) . 
##EQU4## 
If we hold n constant and consider the maximum value of Q, it is seen by 
equation (7) that the value of Q is maximum when m=1/(n+1) . 
##EQU5## 
If we let Q.sub.max be this maximum value of Q, this value is expressed as 
follows. 
##EQU6## 
Therefore, the value of Q cannot be 0.5 or higher. 
Equation (4) can be rewritten in the form of equation (9). Since C.sub.31, 
C.sub.32, R.sub.31, and R.sub.32 are all larger than zero, it is 
impossible for the peak gain H to be 1 or higher. 
##EQU7## 
To achieve superior filter characteristics, it is desirable to have a 
waveform as the output signal v.sub.o that changes sharply with respect to 
frequency, that is, it is desirable that the value of Q be made large. 
Enabling the setting of the peak gain H to a value of 1 or higher is also 
advantageous from the standpoint of circuit design. 
Japanese laid-open patent No. 1989-067015 discloses a filter in that the 
values of quality factor Q and peak gain can be made larger than those of 
the conventional filter described above. This filter, however, includes 
complicated transformer-conductance amplifiers (variable voltage-current 
converters). Further, Japanese laid-open patent No. 1994-283965 discloses 
an active filter without variable voltage-current converters. This filter, 
however, is not an active bandpass filter but an active lowpass filter. 
SUMMARY OF THE INVENTION 
The present invention has as an object the provision of an active bandpass 
filter of simple circuit configuration which offers free setting of the 
value of quality factor Q and peak gain. 
The present invention provides an active bandpass filter having an input 
terminal and an output terminal, comprising: a first transistor having an 
emitter, a base connected to an input terminal via a first resistance 
element, a collector connected both to a constant voltage source via a 
second resistance element and to the output terminal; first means for 
supplying a first constant current to the emitter of the first transistor; 
a second transistor having a base connected to the emitter of the first 
transistor via a third resistance element, a collector connected to the 
constant voltage source via a fourth resistance element and an emitter 
connected to the base of the first transistor via a first capacitance 
element; second means for supplying a second constant current to the 
emitter of the second transistor; a third transistor having a base 
connected to the collector of the second transistor, a collector connected 
to the constant voltage source and an emitter connected to the base of the 
second transistor via a second capacitance element; and third means for 
supplying a third constant current to the emitter of the third transistor. 
The first, second and third means may include a constant current source or 
a resistance element.

DESCRIPTION OF THE PREFERRED EMBODIMENTS 
An embodiment of the present invention will now be described, with 
reference made to the accompanying drawings. 
FIG. 2 is a circuit diagram which shows the configuration of a preferred 
embodiment of an active bandpass filter according to the present 
invention. 
As is shown in FIG. 2, the base of a first bipolar transistor 11 is 
connected to an input terminal 24 via a first resistor 14 having a 
resistance value of R.sub.1. The collector of the transistor 11 is 
connected to a voltage regulator 20 for supplying a constant voltage 
V.sub.1 to the filter via a second resistor 15 having a resistance value 
of R.sub.2 and is also connected to an output terminal 25. In addition, 
the emitter of the transistor 11 is connected to a first constant current 
source 21 for supplying a first constant current I.sub.1 to the transistor 
11. 
The base of a second bipolar transistor 12 is connected to the emitter of 
the transistor 11 via a third resistor 16 having a resistance value of 
R.sub.3. The collector of transistor 12 is connected to the voltage 
regulator 20 via a fourth resistor 17 having a resistance value of 
R.sub.4. The emitter of the transistor 12 is connected to the base of the 
transistor 11 via a first capacitor 18 having a capacitance value of 
C.sub.1 and is also connected to a second constant current source 22 for 
supplying a second constant current I.sub.2 to the transistor 12. 
The base of a third bipolar transistor 13 is connected to the collector of 
the transistor 12. The collector of the transistor 13 is connected to the 
voltage regulator 20. In addition, the emitter of the transistor 13 is 
connected to the base of the transistor 12 via a second capacitor 19 
having a capacitance value of C.sub.2, and is also connected to a third 
constant current source 23 for supplying a third constant current I.sub.3 
to,the transistor 13. 
In the active bandpass filter of FIG. 2, an input signal voltage V.sub.a at 
thee input terminal 24, a base voltage V.sub.b of the transistor 11, a 
base voltage V.sub.c of the transistor 12, a base voltage V.sub.d of the 
transistor 13, and an output signal voltage V.sub.e at the output terminal 
25 are expressed by equations (10) through (13). 
##EQU8## 
Additionally, by virtue of equations (10) through (13), the overall 
transfer function G(e/a) of the active bandpass filter is given by 
equation (14). 
##EQU9## 
The cutoff frequency .omega..sub.0 is expressed by equation (15). 
##EQU10## 
The quality factor Q and peak gain H are given by equation (16) and 
equation (17), respectively. 
##EQU11## 
If C.sub.1 =nC.sub.2, R.sub.1 +R.sub.4 =mR.sub.3 (where n, m&gt;0) are 
substituted into the above-noted equation (15), the cutoff frequency 
.omega..sub.0 is expressed by equation (18), so that the quality factor Q 
is expressed by equation (19). 
##EQU12## 
From equation (19), it can be seen that by appropriately selecting the 
values of n and m (that is, by appropriately selecting the capacitance 
values C.sub.1 and C.sub.2 of the capacitors 18 and 19 and the resistance 
values R.sub.1, R.sub.2, and R.sub.4 of the resistance elements 14, 15, 
and 17, respectively), it is possible to set the quality factor Q freely, 
without limitation. That is, in accordance with this embodiment of the 
present invention, the limitation to a value of Q below 0.5, which is 
imposed in the conventional bandpass filter, is not imposed. 
Furthermore, from the above-noted equation (17), by appropriately selecting 
the respective resistance values R.sub.2 and R.sub.3 of the resistance 
elements 15 and 16, it is possible to set the peak gain H freely, without 
limitation, so that the limitation to a value of peak gain less than 1, 
which is imposed in the conventional bandpass filter, is not imposed. 
FIG. 3 is a schematic circuit diagram which shows another preferred 
embodiment of an active bandpass filter according to the present 
invention. In this figure, elements which are the same as shown in FIG. 2 
are assigned the same reference numerals. 
In the active bandpass filter shown in FIG. 3, the configuration differs 
from the configuration shown in FIG. 2 in that resistors 26, 27, and 28 
are used instead of the first through third constant current sources 21, 
22 and 23. Combination of resistors and constant current sources is also 
available, such as, the current sources 21 and 22 and the resistor 28. 
The cutoff frequency .omega..sub.0, quality factor Q, and peak gain H given 
by equations (15) through (19) can be achieved even in the case in which 
resistors are used instead of constant current sources, enabling 
achievement of the desired effect of the present invention. 
As described in detail above, in accordance with the present invention, an 
active bandpass filter offering free setting of the values of quality 
factor Q and peak gain is provided.