Fully Controllable First Order Current Mode Universal Filter Composed of BJTs and a Grounded Capacitor

In the last two decades, current-mode (CM) circuits have received more attention. These types of circuits offer many advantages such as wider bandwidth, bigger dynamic range, better linearity and more IC suitability when compared with voltage mode (VM) topologies [1, 2]. In addition to this, electronic tunability is also one of the other important issues in electronic design since it allows us to control characteristics of circuit easily, i.e. resonance frequency of filter [3]. In a tunable circuit, electronically control can be achieved via biasing currents in BJT technology. In the literature, many CM and VM filters have been presented [4-10]. However, some of the reported circuits suffer from shortcoming of electronic tunability [5]. Quite a large number of filters composed of basic building block(s) such as current conveyors were also previously reported whereas each of the blocks use tens of transistors [3-8]. This paper presents an electronically tunable CM first order universal filter employing only a grounded capacitor and fewer BJTs [11] when compared with previously published ones. The proposed filter can produce all the standard filter functions i.e. low-pass, high-pass and allpass filters. Cut-off frequency can be tunable and filter types can also be controllable by simply changing the values of some current sources. The introduced circuit is free from critical passive component matching conditions and cancellation constraints, and provides high output impedance yielding easy cascadability. Moreover, second order band-pass filter obtained by cascading low-pass filter and high-pass filter is also presented as an application. The validity of proposed filter is verified through PSpice simulations.


Introduction
In the last two decades, current-mode (CM) circuits have received more attention.These types of circuits offer many advantages such as wider bandwidth, bigger dynamic range, better linearity and more IC suitability when compared with voltage mode (VM) topologies [1,2].In addition to this, electronic tunability is also one of the other important issues in electronic design since it allows us to control characteristics of circuit easily, i.e. resonance frequency of filter [3].In a tunable circuit, electronically control can be achieved via biasing currents in BJT technology.In the literature, many CM and VM filters have been presented [4][5][6][7][8][9][10].However, some of the reported circuits suffer from shortcoming of electronic tunability [5].Quite a large number of filters composed of basic building block(s) such as current conveyors were also previously reported whereas each of the blocks use tens of transistors [3][4][5][6][7][8].
This paper presents an electronically tunable CM first order universal filter employing only a grounded capacitor and fewer BJTs [11] when compared with previously published ones.The proposed filter can produce all the standard filter functions i.e. low-pass, high-pass and allpass filters.Cut-off frequency can be tunable and filter types can also be controllable by simply changing the values of some current sources.The introduced circuit is free from critical passive component matching conditions and cancellation constraints, and provides high output impedance yielding easy cascadability.Moreover, second order band-pass filter obtained by cascading low-pass filter and high-pass filter is also presented as an application.The validity of proposed filter is verified through PSpice simulations.

Proposed First-Order Universal Filter
A generalized first order transfer function is given in (1).Type of a filter is determined by the coefficients and , e.g.low pass, high pass, etc.
Many techniques are available to design a filter from transfer function of system.One of them is known as block diagram technique.It is easy to rearrange system by obeying manipulation rules in accordance with design purposes.Moreover, it is very simple way to construct complicate systems by using functional blocks.Let's multiply with (− ) numerator and denominator of the transfer function Output current can be defined as given in (3) In these equations, is constant term while and depicts resistance value and capacitance value respectively.
Next step of designing first order filter is mapping on coefficients of generalized first order filter transfer function given in (1) to obtain appropriate system equations to realize function by using BJTs and a grounded capacitor.For this purpose, each coefficient of numerator of transfer function is assigned to a function.It should be noted that by using this way general characteristics of system remains unchanged.
Let's assume = ( − ) and = yields input current and output current as given in ( 7) and ( 8) respectively: These system equations can be considered as node equations.Both of two equations have scaling terms multiplied with input current.As mentioned above, these terms consists of numerator's coefficients of transfer function can be controlled by tuning some dc current sources.It means that type of first order filter can be selected electronically.
The expression of is given clearly in (9).This current which is key aspect of design consist of two constant terms, , cut off frequency, , the value of capacitor, and one time varying term, , the value of node voltage.Cut off frequency of proposed first order filter is given in (10): A block diagram of representation of system is given in Fig. 1.The block diagram consists of functional blocks of generalized first order filter function and summing blocks.There are three types of functional blocks, namely multiplying constant term block used to acquire electronically tunability, current to voltage converter block and differentiator block which is also used for voltage to current converter.In order to realize constant multiplying block which plays essential role for synthesizing electronically tunable system, static translinear circuit structure are employed [12][13][14].By selecting and all first order filter types can be produced as given in Table 1.It means that this advantage give us wide area of usage without modification on circuit architecture.It is also offers economic reasons to use of this circuit which have ability of electronically controllability since same manufactured circuit can be used for many purpose.The proposed first order universal filter employing BJTs, a grounded capacitor and some current sources, shown in Fig. 2, consists of three parts, main circuit, translinear loops, and current mirror.As mentioned above, the proposed filter has capability of to tune cut off frequency and to select filter type.Input current of circuit composed of both input signal and dc bias current depicts pole frequency.Q 2 , Q 3 and Q 5 transistors are operating in active region and biased as given in Table 2 for all filter responses.

Table 2. Types of filters due to bias currents of BJTs
Type of filter One of the applications of the realized first order universal filter is second order band-pass filter employing only grounded and canonical number of capacitors and BJTs, which is shown in Fig. 3. Essentially, this filter is obtained by cascading first order low-pass filter and first order high-pass filter.

Simulation Results
In order to confirm the theoretical results detailed previous section, the proposed first order universal filter is simulated in the PSpice program by using both ideal BJT obtained by employing default BJT model with = 10000 and CBIC-R model [10].Obtained simulation results show that theoretical design is verified.The value of capacitance of filter circuit is chosen to be = 10 .The numbers of simulations are performed including time domain analysis and frequency domain analysis.The total power dissipation is found as 28. 4 .First of all, the frequency responses of all possible filter characteristics are obtained.The gain characteristics of fundamental first order filter responses; high-pass, lowpass and all-pass are given in Fig. 4. As seen from the figure, the simulated and ideal results are in accordance with each other.The values of current sources are set to be as given in Table 2 for each filter.In order to show that electronic tunability capability of the proposed filter, many simulations are performed on cut off frequencies of all filter responses.In Fig. 5 phase responses of all-pass filter for various dc current values are given.Fig. 6 points out cut off variations due to dc current value.Control dc current is tuned from = 50 to = 1 that yields cut off frequency of all-pass filter is swept approximately more than one decade.Total harmonic distortion (THD) of output signal of the proposed filter circuit is also measured when sinusoidal input signal is applied.Characteristics of input signal and dc operating point defines cut off frequency and measured THD values for all filter responses are depicted in Table 3. Simulated second-order band-pass filter response is drawn as shown in Fig. 7 in which bias currents of both filter is selected as equal to each other.Gain response of each block, low-pass filter block and high-pass filter block is given in the figure, as well.

Conclusions
In this work, a current mode first order universal filter circuit is presented by obeying block diagram synthesis method.This circuit has many advantages such as capability of not only electronically tunability but also electronically controllability while it offers low component count structure when compared to published ones.Moreover, these features can be attained simply and correctly by changing the values of dc current sources.Additionally, second order band-pass filter is presented as an application example which is obtained by cascading two first order filters.Theoretical design background is also verified through PSpice simulator program.All obtained results are given and discussed in related section.It should be noted that a significant contribution is made to analog electronic by designing this universal circuit.

Fig. 1 .
Fig. 1.Block diagram of representation of system

Fig. 3 .
Fig.3.Proposed second order band-pass filter derived from the first order universal filter given in Fig.2

Fig. 4 .
Fig. 4. Gain responses of all first order filters

Fig. 5 .
Fig. 5. Phase responses of all-pass filter for various

Fig. 6 .Table 3 . 44952 Fig. 7 .
Fig. 6.Electronic tuning of pole frequencies with respect to control currentTable 3. THD values of all filter responses and information Characteristic Value 500 Peak value of input signal 100 Frequency of input signal 1 %THD for high-pass response 0.3801355 %THD for low-pass response 1.277466 %THD for all-pass response 1.44952

Table 1 .
Types of filters and their characteristics via control variables ,