Electronically Tunable Current Controlled Current Conveyor Transconductance Amplifier-Based Mixed-Mode Biquadratic Filter with Resistorless and Grounded Capacitors

Abstract: A new electronically tunable mixed-mode biquadratic filter with three current controlled current conveyor transconductance amplifiers (CCCCTAs) and two grounded capacitors is proposed. With current input, the filter can realise lowpass (LP), bandpass (BP), highpass (HP), bandstop (BS) and allpass (AP) responses in current mode and LP, BP and HP responses in transimpedance mode. With voltage input, the filter can realise LP, BP, HP, BS and AP responses in voltage and transadmittance modes. Other attractive features of the mixed-mode biquadratic filter are (1) the use of two grounded capacitors, which is ideal for integrated circuit implementation; (2) orthogonal control of the quality factor (Q) and resonance angular frequency (ωo) for easy electronic tenability; (3) low input impedance and high output impedance for current signals; (4) high input impedance for voltage signal; (5) avoidance of need for component-matching conditions; (6) resistorless and electronically tunable structure; (7) low active and passive sensitivities; and (8) independent control of the voltage transfer gains without affecting the parametersωo and Q.


Filters
No. of Active Elements No. of Passive Elements Composed of Equivalent Active Elements [13] Table 2. Characteristic comparisons with previous reported mixed-mode filters.

Filters
Properties1 (1) [13] no no no no no yes yes yes yes [14] no no no no no yes no yes yes [15] no no no no no yes no yes yes [16] no no no yes yes yes yes no yes [17] no yes no no no yes yes no yes [18] no no no no no yes yes no no [19] no no no no no no no no yes [20] yes no no no yes yes yes yes yes [21] yes no no no yes yes yes no yes [22] yes no no no yes yes no no yes [23] yes no no yes yes yes no no yes [24] yes yes no no no yes yes no yes [25] yes yes no yes no yes no no yes [26] yes yes no no yes yes no no yes [27] yes yes no yes yes yes yes no yes this work yes yes yes yes yes yes yes yes yes 1 (1) resistorless and electronically tunable structure; (2) simultaneous realisation of three generic filtering responses in all the four possible modes; (3) capability to realise bandstop and allpass filtering responses in the voltage mode, current mode and transadmittance mode without critical component-matching conditions; (4) low-input and high-output impedances for current signals; (5) high-input impedance for voltage signal; (6) use of only grounded capacitors; (7) orthogonal control of the parameters quality factor (Q) and resonance angular frequency (ω o ) of the filter; (8) independent control of the voltage mode filter gains without affecting the parameters Q and ω o ; and (9) low active and passive sensitivity performances.

Basic Concept and Implementation of the CCCCTA
The CCCCTA simplifies circuit implementation by providing an active building block.The CCCCTA device is obtained by cascading the CCCII with the OTA to implement analogue function circuits in compact monolithic chips [28,29].This versatile component also has potential applications in analogue signal-processing circuits.Because its parasitic resistance and transconductance can be adjusted electronically by the input bias currents I S and I B , respectively, it does not require a resistor in practical applications, which is an attractive feature for filter designers.Figure 1 shows the circuit symbol of the CCCCTA [29].The port relations of CCCCTA can be characterized by the following matrix equation [26][27][28][29]: where R x and g m are the parasitic resistance at X-terminal and the transconductance gain of the CCCCTA, respectively.The parasitic resistance R x can be controlled by the bias current I S of CCCCTA, and the transconductance gain g m can be controlled by the bias current I B of CCCCTA.

Input Voltage at High
Input Impedance

Input Current at Low Input Impedance
Output Current at High Output Impedance [26] AP yes no yes [27] AP yes yes yes this work nil yes yes yes 1 AP: allpass.

Basic Concept and Implementation of the CCCCTA
The CCCCTA simplifies circuit implementation by providing an active building block.The CCCCTA device is obtained by cascading the CCCII with the OTA to implement analogue function circuits in compact monolithic chips [28,29].This versatile component also has potential applications in analogue signal-processing circuits.Because its parasitic resistance and transconductance can be adjusted electronically by the input bias currents IS and IB, respectively, it does not require a resistor in practical applications, which is an attractive feature for filter designers.Figure 1 shows the circuit symbol of the CCCCTA [29].The port relations of CCCCTA can be characterized by the following matrix equation [26][27][28][29]: where Rx and gm are the parasitic resistance at X-terminal and the transconductance gain of the CCCCTA, respectively.The parasitic resistance Rx can be controlled by the bias current IS of CCCCTA, and the transconductance gain gm can be controlled by the bias current IB of CCCCTA.CCCCTA (current controlled current conveyor transconductance amplifier) symbolic representation.

Proposed Electronically-Tunable Mixed-Mode Biquadratic Filter
Figure 2 shows that the proposed electronically tunable mixed-mode biquadratic filter employs three CCCCTAs and two grounded capacitors.The multiple current outputs of the CCCCTA are easily implemented by adding output branches to the CCCCTA.The input current of the circuit is applied to the X-terminal of the first CCCCTA, which has low input impedance.The output currents are obtained at high output impedance ports, which simplifies cascading in both CM and TAM operations.The input voltage of the circuit is applied to the Y-terminal of the third CCCCTA, which has high input impedance.Because the circuit has low input impedance and high output impedance for current signals and has high input impedance for voltage signal, it can be used in cascade for realizing higher-order filters [16].Moreover, grounded capacitors are used in integrated circuits to cancel parasitic impedance effects of active elements [16].Routine analysis of the circuit in Figure 2 reveals that the following four output voltages and five output currents can be obtained.
Appl.Sci.2017, 7, 244 6 of 24 Equations ( 12)-( 15) indicate that a non-inverting HP filtering response is obtained from Io1, an inverting BP filtering response is obtained from Io2, a non-inverting LP filtering response is obtained from Io3, and two non-inverting BP filtering responses are obtained from Io4 and Io5.The BS where G X1 = 1 R X1 , G X2 = 1 R X2 , and G X3 = 1 R X3 .

CM and TIM
According to Equations ( 2)-( 10), CM and TIM can be obtained by setting the input voltage V in = 0 (grounded) and getting I in as input signal.The five current transfer functions obtained are: Equations ( 12)- (15) indicate that a non-inverting HP filtering response is obtained from I o1 , an inverting BP filtering response is obtained from I o2 , a non-inverting LP filtering response is obtained from I o3 , and two non-inverting BP filtering responses are obtained from I o4 and I o5 .The BS filtering response is easily obtained by adding the two currents I o1 and I o3 to obtain the following transfer function: Similarly, the AP transfer function is easily obtained by adding the three currents I o1 , I o2 and I o3 to obtain the following transfer function: Thus, all five standard filtering responses are provided by the same CM biquadratic filter structure, and no other component-matching conditions are needed.Notably, all current outputs are available from high-output impedance terminals.High-output impedance terminals of the configuration enable the circuit to be cascaded without additional current buffers.Because the gain of the current-mode HP, LP and BP filters is unity, the additional current amplifiers are needed if a variable gain of current-mode filter is necessary.In addition, the BS and AP filters cannot be realised simultaneously with the HP, LP and BP filters.This problem can be solved by adding the multiple current outputs that can be easily implemented by simply adding output branches.
According to Equation (11), filter parameters ω o and Q are: Based on Equation (18), parameter Q can be independently tuned by using g m1 without disturbing ω o .Restated, parameters ω o and Q are orthogonally adjustable through the finite input conductance G X2 and then the g m1 in that order.This property is desirable in biquadratic filters because it increases design and tuning flexibility.
Accordingly, the four TIM transfer functions in this case can be obtained as follows: As indicated by Equations ( 19)-( 22), an inverting LP filtering response is obtained from V o1 , an inverting BP filtering response is obtained from V o2 , a non-inverting HP filtering response is obtained Appl.Sci.2017, 7, 244 8 of 22 from V o3 , and a non-inverting BP filtering response is obtained from V o4 .That is, the circuit provides TIM HP, LP and two BP responses simultaneously without disturbing circuit topology.

VM and TAM
According to Equations ( 2)-( 10), VM and TAM can be obtained by setting the input voltage I in = 0 (opened) and getting V in as input signal.The four voltage transfer functions obtained are: As indicated by Equations ( 23)-( 26), a non-inverting LP filtering response is obtained from V o1 , a non-inverting BP filtering response is obtained from V o2 , an inverting HP filtering response is obtained from V o3 , and a non-inverting BS filtering response is obtained from V o4 .Notably, connecting the output current signal I o5 to the output voltage node V o4 also obtains a non-inverting AP transfer function in VM as follows: The gain constants in Equations ( 23)-( 26) are In Equation ( 18), the proposed filter orthogonally controls ω o and Q by tuning conductance G X2 for ω o and then tuning transconductance gain g m1 for Q without disturbing parameter ω o .According to Equation (28), the VM filter transfer gains can be independently controlled by changing G X3 without affecting ω o and Q, and the finite input conductance G X3 at the X-terminal of the CCCCTA(3) is tunable.Therefore, the VM filter provides orthogonal tunability of all three filter parameters (ω o , Q and H o ) in all five responses.This is because the three output voltages V o1 , V o2 and V o4 are not in low-output impedance terminals.Voltage followers are needed for the proposed circuit to drive low impedance loads or to be directly connected to the next stages.
Accordingly, the five TAM transfer functions in this case are obtained as follows: As indicated by Equations ( 29)-( 33), an inverting HP filtering response is obtained from I o1 , a non-inverting BP filtering response is obtained from I o2 , an inverting LP filtering response is obtained from I o3 , a non-inverting BS filtering response is obtained from I o4 and an inverting BP filtering response is obtained from I o5 .Thus, the proposed filter can simultaneously realise LP, BP, HP and BS responses in TAM.The TAM AP transfer function is easily obtained by adding currents I o4 and I o5 , which yields the following transfer function: Table 5 summarizes the four possible modes of the transfer functions according to Equations ( 2)- (10).
Table 5. Input conditions and various functions realised.

Filter function
V in = 0, I in is Input Signal * A non-inverting AP voltage-mode transfer function is easily obtained by connecting the output current signal I o5 to the output voltage node V o4 .

Non-Ideal Analysis and Sensitivity Performance
If the non-idealities of CCCCTA are considered, the relationships of the terminal voltages and currents can be rewritten as V X = βV Y + I X R X , I Z+ = α p I X , I Z− = −α n I X , I O1 = γ p g m V Z+ , I −O1 = −γ n g m V Z+ , I O2 = η p g m V Z+ and I −O2 = −η n g m V Z+ , where β, α p , α n , γ p , γ n , η p and η n are CCCCTA transfer ratios that deviate from unity by the transfer errors [27].In a non-ideal case with reanalysis of the proposed circuit in Figure 2, the denominator of the non-ideal voltage transfer function is yielded as follows: where β i , α pi and γ pi are the parameters β, α p and γ p , respectively, of the ith CCCCTA (i = 1, 2, 3).The non-ideal expressions for ω o and Q are obtained as follows: The active and passive sensitivities of the proposed circuit are These calculation results indicate that all sensitivities are low and have absolute values no larger than unity.The proposed circuit thus exhibited low sensitivity.

Effect of the CCCCTA Parasitic Impedances and Design Considerations
Next, various parasitic impedances of the CCCCTA in the proposed circuit were studied.Figure 3 represents the non-ideal CCCCTA model including its parasitic elements.A port Y parasitic is in the form R Yi //C Yi , a port Z+ parasitic is in the form R Zi+ //C Zi+ , a port Z− parasitic is in the form R Zi− //C Zi− , a port O 1 parasitic is in the form R O1i //C O1i , a port O 2 parasitic is in the form R O2i //C O2i , a port -O 1 parasitic is in the form R -O1i //C -O1i , a port -O 2 parasitic is in the form R -O2i //C -O2i , and a port X parasitic is in the form R Xi where i = 1, 2, 3 and indicates the ith CCCCTA.After applying the non-ideal equivalent circuit mode of the CCCCTA in the proposed circuit, the denominator of the transfer functions becomes: where, Appl.Sci.2017, 7, 244 10 of 24 , and Equations ( 41)-( 43) illustrate that the effects of parasitic elements depend on three parasitic poles yielded by the non-idealities of CCCCTAs.For near-ideal frequency operation, the operating frequency must be higher than ω1 and ω2 and lower than ω3.Therefore, the useful frequency range of the proposed filter is limited by the following conditions: This condition is easily satisfied since the external capacitance can be set much higher than the parasitic capacitance.In Figure 2, the effects of CCCCTA parasitic elements on the proposed filter can be ignored under the following conditions: min (C1, C2) >> parasitic capacitances (CZ1+, CZ2+, CY2), parasitic resistances (RO11, RO12, RZ3−) >> RX1, 1/sC1 << RZ2+ and 1/sC2 << RZ1+//RY2.
According to (44), the effects of parasitic elements on coefficients n1, n2 and m diminish under the conditions Equations ( 41)-( 43) illustrate that the effects of parasitic elements depend on three parasitic poles yielded by the non-idealities of CCCCTAs.For near-ideal frequency operation, the operating frequency must be higher than ω 1 and ω 2 and lower than ω 3 .Therefore, the useful frequency range of the proposed filter is limited by the following conditions: This condition is easily satisfied since the external capacitance can be set much higher than the parasitic capacitance.In Figure 2, the effects of CCCCTA parasitic elements on the proposed filter can be ignored under the following conditions: min (C 1 , C 2 ) >> parasitic capacitances (C Z1+ , C Z2+ , C Y2 ), parasitic resistances (R O11 , R O12 , R Z3− ) >> R X1 , 1/sC 1 << R Z2+ and 1/sC 2 << R Z1+ //R Y2 .
According to (44), the effects of parasitic elements on coefficients n 1 , n 2 and m diminish under the conditions |s| >> ω 1 , |s| >> ω 2 and |s| << ω 3 .Hence, By substituting Equations ( 45)-(47) into Equation ( 40) and assuming that (R O11 , R O12 , R Z3− ) >> R X1 , the characteristic equation is: In this case, ω o and Q become: Thus, the effects of CCCCTA parasitic elements on the proposed filter in Figure 2 can be ignored in this case.

Pre-Layout Simulation
The performance of the proposed circuit was evaluated by an H-Spice simulation in a Taiwan Semiconductor Manufacturing Company (TSMC) 0.18-µm process.Figure 4 shows the complementary metal oxide semiconductor (CMOS) implementation of a CCCCTA [29].The multiple current outputs are easily implemented by simply adding output branches.Table 6 gives the dimensions of the metal oxide semiconductor (MOS) transistors used in the CCCCTA implementation.The supply voltages are V DD = −V SS = 0.9 V. To obtain a pole frequency of f o = 3.183 MHz at Q = 1, the active and passive components were set to I B1 = I B2 = I B3 = 24.135µA (g m = 100 µS), I S1 = I S2 = I S3 = 1.778 µA (R X = 10 kΩ) and C 1 = C 2 = 5 pF. Figure 5 represents the simulated frequency responses for the HP (I o1 ), BP (I o2 ), LP (I o3 ) and BP (I o4 ) filters in the CM. Figure 6 represents the simulated frequency responses for the LP (V o1 ), BP (V o2 ), HP (V o3 ) and BS (V o4 ) filters, respectively, in the VM. Figure 7 represents the VM non-inverting AP (V o4 ) simulated frequency response when the output current signal I o5 is connected to the output voltage node V o4 .Figure 8 represents the simulated frequency responses for the HP, BP, LP and BS filters in the TAM. Figure 9 represents the simulated frequency responses for the LP, BP, HP and BS filters in the TIM.7 gives the different I B1 and I S3 values used in Figure 10.The Table 7 shows that Q can be used to adjust the input bias current I B1 without affecting the f o as depicted in Equation (18) and that the BP (V o2 ) transfer gains can be independently controlled by changing I S3 without affecting the f o .Figure 11 represents the VM gain responses of the BP filter.The I B and I S values were changed by maintaining a constant ratio for constant Q.Table 8 shows the component values and corresponding ideal and simulated pole frequencies.The calculation results show that the f o can be adjusted without affecting the Q.The input dynamic range of the VM filter was tested by repeating the simulation for a sinusoidal input signal at f o = 3.183 MHz. Figure 12a shows the input dynamic range of the BP filter at the V o2 output terminal with I B1 = I B2 = I B3 =96.5 µA (g m = 200 µS), I S1 = I S2 = I S3 = 7.113 µA (R X = 5 kΩ) and C 1 = C 2 = 10 pF, which extended to an amplitude of 0.5 V (peak to peak) without signification distortion.In Figure 12a, the percentage of

Post-Layout Simulation
The layout of the entire schematic was done using cadence's virtuoso tool.Figures 13 and 14 show the overall chip layout and the detail layout of the filter core, respectively.The layout floorplan is shown in Figure 15 which explains element placement.The component values of Figures 13 and 14 were given by gm = 100 μS, RX = 10 kΩ and C1 = C2 = 5 pF, leading to a center frequency fo = 3.183 MHz.

Post-Layout Simulation
The layout of the entire schematic was done using cadence's virtuoso tool.Figures 13 and 14 show the overall chip layout and the detail layout of the filter core, respectively.The layout floorplan is shown in Figure 15 which explains element placement.The component values of Figures 13 and 14 were given by g m = 100 µS, R X = 10 kΩ and C 1 = C 2 = 5 pF, leading to a center frequency f o = 3.183 MHz.A design rules check (DRC) and a layout versus schematic (LVS) comparison were performed on the layout.The DRC checks for potential errors in the layout.The LVS checks the layout against the schematic and verifies that all the nets are matching.After the DRC and LVS were completed successfully, layout extraction was done.The extraction gives an overall idea about the parasitics of the design.All these processes are carried out using a cadence virtuoso schematic and layout editor tool for TSMC 0.18-µm CMOS process technology.The post-layout simulations were carried out to check the functionality of the design.Figure 16 represents the post-layout simulated frequency responses for the HP (I o1 ), BP (I o2 ), LP (I o3 ) and BP (I o4 ) filters in the CM.The post-layout simulation results show the CM simulated natural frequency as 3.10 MHz, that is, an approximately 2.52% error with the theoretical value.Figure 17 represents the post-layout simulated frequency responses for the LP (V o1 ), BP (V o2 ), HP (V o3 ) and BS (V o4 ) filter in the VM.The post-layout simulation results show the VM simulated natural frequency as 3.08 MHz, that is, an approximately 3.14% error with the theoretical value.Figure 18 represents the post-layout simulated frequency responses for the HP (I o1 ), BP (I o2 ), LP (I o3 ) and BS (I o4 ) filter in the TAM.The post-layout simulation results show the TAM simulated natural frequency as 3.10 MHz, that is, an approximately 2.52% error with the theoretical value.Figure 19 represents the post-layout simulated frequency responses for the LP (V o1 ), BP (V o2 ), HP (V o3 ) and BP (V o4 ) filter in the TIM.The post-layout simulation results show the TIM simulated natural frequency as 3.09 MHz, that is, an approximately 2.83% error with the theoretical value.It appears from Figures 16-19 that the filter post-layout simulation performs all the filter functions well, but the small departures filter responses mainly stems from the parasitic impedance effects and non-ideal gains of the CCCCTA.The total power dissipation is found to be 0.593 mW.The chip area without pads is only 0.5177 × 0.4507 mm 2 .
responses for the HP (Io1), BP (Io2), LP (Io3) and BP (Io4) filters in the CM.The post-layout simulation results show the CM simulated natural frequency as 3.10 MHz, that is, an approximately 2.52% error with the theoretical value.Figure 17 represents the post-layout simulated frequency responses for the LP (Vo1), BP (Vo2), HP (Vo3) and BS (Vo4) filter in the VM.The post-layout simulation results show the VM simulated natural frequency as 3.08 MHz, that is, an approximately 3.14% error with the theoretical value.Figure 18 represents the post-layout simulated frequency responses for the HP (Io1), BP (Io2), LP (Io3) and BS (Io4) filter in the TAM.The post-layout simulation results show the TAM simulated natural frequency as 3.10 MHz, that is, an approximately 2.52% error with the theoretical value.Figure 19 represents the post-layout simulated frequency responses for the LP (Vo1), BP (Vo2), HP (Vo3) and BP (Vo4) filter in the TIM.The post-layout simulation results show the TIM simulated natural frequency as 3.09 MHz, that is, an approximately 2.83% error with the theoretical value.It appears from Figures 16-19 that the filter post-layout simulation performs all the filter functions well, but the small departures filter responses mainly stems from the parasitic impedance effects and non-ideal gains of the CCCCTA.The total power dissipation is found to be 0.593 mW.The chip area without pads is only 0.5177 × 0.4507 mm 2 .

Figure 3 .
Figure 3. Non-ideal equivalent circuit model of the CCCCTA.

Figure 3 .
Figure 3. Non-ideal equivalent circuit model of the CCCCTA. C Figure 10 represents VM gain responses of BP (V o2 ) filter for different I B1 and I S3 values, by keeping I B2 = I B3 = 24.135µA, I S1 = I S2 = 1.778 µA and C 1 = C 2 = 5 pF.The Q varied (1, 2, 5 and 10) when f o was maintained at 3.183 MHz.Table

Figure 12 .
Figure 12.Time-domain results of VM bandpass filter at the output Vo2 of Figure 2 (a) input (blue line) and output (red line) waveforms; (b) total harmonic distortion (THD) analysis results on input voltage at 3.183 MHz.

Figure 12 .
Figure 12.Time-domain results of VM bandpass filter at the output V o2 of Figure 2 (a) input (blue line) and output (red line) waveforms; (b) total harmonic distortion (THD) analysis results on input voltage at 3.183 MHz.

Figure 13 .
Figure 13.The layout of the proposed mixed-mode biquadratic filter chip.Figure 13.The layout of the proposed mixed-mode biquadratic filter chip.

Figure 14 .
Figure 14.The core of the proposed mixed-mode biquadratic filter.

Table 1 .
Comparison of previously reported mixed-mode filters.1

Table 6 .
The aspect ratios of the CMOS transistors in CCCCTA implementation.

Table 8 .
Component values used to obtain a specified fo.