Electronically Tunable Quadrature Oscillator Using Grounded Components with Current and Voltage Outputs

Abstract

The electronically tunable quadrature oscillator using a single multiple-output current controlled current differencing transconductance amplifier (MO-CCCDTA) and grounded passive components is presented. The proposed configuration uses a single MO-CCCDTA, two grounded capacitors and one grounded resistor. Two high-output impedance quadrature current signals and two quadrature voltage signals with 90° phase difference. The oscillation condition and oscillation frequency of the proposed quadrature oscillator are independently controllable. The use of only grounded passive components makes the proposed circuit ideal for integrated circuit implementation.

1. Introduction

At present, there is a growing interest in designing analogue current-mode signal-processing circuits. Various new current-mode active building blocks have received considerable attentions owing to their larger dynamic range, greater linearity, wider bandwidth, and low power consumption with respect to operational amplifier-based circuits [1–6]. As a result, current-mode active components have been increasingly used to realize active filters and sinusoidal oscillators. Single-element-controlled sinusoidal oscillators find numerous applications in communication, control systems, signal processing, instrumentation, and measurement systems as test oscillators or signal generators [7–11]. A quadrature oscillator is used because the circuit simultaneously provides two sinusoids with 90° phase difference for a variety of applications, such as in telecommunications for quadrature mixers, in single-sideband generators, and in direct-conversion receivers or for measurement purposes in vector generators or selective voltmeters [11]. Quadrature signals are an essential part of modern RF-communication architectures such as zero-IF and image-reject receivers [12]. The quadrature oscillator described in [13] was developed for its possible use within a soil-impedance measurement system.

In 2003, a new current-mode active element that is called current differencing transconductance amplifier (CDTA) was introduced [14]. It has a pair of low-impedance current inputs 𝑝 and 𝑛 and an auxiliary terminal 𝑍, whose outgoing current is the difference of input currents [15]. Owing to the current conveying, the CDTA is one of the modifications of the current conveyor. This element, connected with some external passive components, makes it possible to build many important applications like filters [16, 17] and oscillators [18, 19]. Many modifications of CDTA structure can be found in the literature. For example, duplication of the 𝑍 terminal is discussed in [20, 21], replacement of the transconductance amplifier with the voltage follower is discussed in [22], and replacement of the current differencing stage with the current buffer is discussed in [23]. In 2011, a new kind of resistorless voltage-mode and current-mode quadrature sinusoidal oscillator using a single differential voltage current-controlled conveyor transconductance amplifier (DVCCTA) and two grounded capacitors has been proposed [24]. The circuit provides two explicit quadrature current outputs and two quadrature voltage outputs, simultaneously. The oscillation condition and oscillation frequency are independently controllable. However, no voltage-mode and current-mode quadrature oscillator circuit based on single multiple-output current controlled current differencing transconductance amplifier (MO-CCCDTA) has been proposed which simultaneously provides two explicit quadrature current outputs and two quadrature voltage outputs in the same configuration. Recently, an electronically controllable current-mode quadrature oscillator using a single MO-CCCDTA as the active element has been introduced [25], in which the operational transconductance amplifiers (OTAs) at the two output ports can be controlled by an external bias current. This proposed circuit employs a single MO-CCCDTA, two grounded capacitors, and one grounded resistor and offers the advantages of (i) independent control of condition of oscillation (CO) and frequency of oscillation (FO) and (ii) low active and passive sensitivities. However, one of the current outputs is available on a grounded capacitor. One requires additional current follower for sensing and taking out the quadrature current output therein. The use of additional current follower with the virtual grounded input may result in floating capacitor realization for what is originally described as grounded capacitor realization.

In this paper, the author also proposes another simple electronically controllable grounded capacitor quadrature oscillator using a single MO-CCCDTA. The proposed circuit has all of the advantages by Prasad et al. [25] in addition to one more advantage of high-output impedance current outputs without using additional current followers. Both current-mode and voltage-mode quadrature signals can be simultaneously obtained in the proposed circuit. Sinusoidal oscillators which produce both current and voltage output signals are useful for their versatility. Since the proposed circuit consists of single MO-CCCDTA and all grounded passive components, it is more suitable for integrated circuit implementation.

2. Proposed Current-Mode and Voltage-Mode Quadrature Oscillator

MO-CCCDTA is relatively new active element [25] and has received considerable attention as current-mode active element. The MO-CCCDTA design concept originated from the CDTA [14]. The circuit symbol of the MO-CCCDTA is shown in Figure 1 [25]. It consists of two well-known and mutually independent building blocks, namely, 𝑍 copy CDTA and dual-output OTA. OTA is relatively independent. The MO-CCCDTA with multiple 𝑍 and 𝑋 terminals has been used to create the quadrature oscillator. The terminal characteristics of the MO-CCCDTA are given by 𝑉_𝑝=𝑉_𝑛=0, 𝐼_𝑍1=𝐼_𝑍2=𝐼_𝑝−𝐼_𝑛, 𝐼_𝑋1+=𝑔_𝑚1𝑉_𝑍1, 𝐼_𝑋1−=−𝑔_𝑚1𝑉_𝑍1, 𝐼_𝑋2+=𝑔_𝑚2𝑉_𝑍2, and 𝐼_𝑋2−=−𝑔_𝑚2𝑉_𝑍2, where 𝑉_𝑧=𝐼_𝑍𝑍_𝑧 and 𝑍_𝑧 is the external impedance connected to the 𝑍 terminal of the CDTA [25]. 𝐼_𝐵3 and 𝐼_𝐵4 indicated in Figure 1 show the external bias currents which control the transconductances to make the circuit electronically controllable [25]. The proposed current-mode and voltage-mode quadrature oscillator is shown in Figure 2. It is based on a single MO-CCCDTA, two grounded capacitors, and one grounded resistor. The use of only grounded passive components makes the proposed circuit ideal for integrated circuit implementation. Routine analysis of the proposed oscillator circuit of Figure 2 yields the following characteristic equation: 𝐷(𝑠)=𝑠²𝐶₁𝐶₂𝑅₁+𝑠𝐶₂1−𝑔_𝑚1𝑅₁+𝑔_𝑚1𝑔_𝑚2𝑅₁. (1)

Figure 1 

MO-CCCDTA symbol [25].

Figure 2 

The proposed current-mode and voltage-mode quadrature oscillator.

From (1), the CO is 𝑔_𝑚1𝑅₁=1 (2) and the FO is 𝑓_𝑜=12𝜋𝑔_𝑚1𝑔_𝑚2𝐶₁𝐶₂. (3) As indicated by (2) and (3), the CO can be controlled independently of FO by changing 𝑅₁; the FO can be controlled by 𝑔_𝑚2 and hence it is current controllable by bias current 𝐼_𝐵4. From Figure 2, under steady state, the relationships between output currents 𝐼_𝑜1 and 𝐼_𝑜2 are 𝐼_𝑜1=𝜔_𝑜𝐶₁𝑔_𝑚2𝑒^−𝑗90∘𝐼_𝑜2 (4) ensuring the currents 𝐼_𝑜2 and 𝐼_𝑜1 to be in quadrature.

The relationships between output voltages 𝑉_𝑜1 and 𝑉_𝑜2 are 𝑉_𝑜1=𝜔_𝑜𝐶₂𝑔_𝑚1𝑒^𝑗90∘𝑉_𝑜2 (5) ensuring the voltages  𝑉_𝑜2 and 𝑉_𝑜1 to be in quadrature.

Clearly, the current-mode and voltage-mode quadrature signals can be simultaneously obtained from Figure 2. Because the output impedances of the currents 𝐼_𝑜1 and 𝐼_𝑜2 in Figure 2 are very high, the two output terminals, 𝐼_𝑜1 and 𝐼_𝑜2, can be directly connected to the next stage. It should be noted that the two quadrature voltages are to be buffered before use. This would require larger area on the chip and more power consumption. To the best of author’s knowledge, no single active element oscillator is proposed till date that simultaneously provides explicit quadrature current outputs and buffered voltage outputs, without using external voltage buffers.

3. Nonideality Analysis and Design Considerations

Taking the nonidealities of the MO-CCCDTA into account, the relationship of the terminal voltages and currents can be rewritten as 𝐼_𝑍𝑖=𝛼_𝑝𝑖𝐼_𝑝−𝛼_𝑛𝑖𝐼_𝑛 for 𝑖=1,2, 𝑉_𝑝=𝑉_𝑛=0, 𝐼_𝑋1+=𝛽₁𝑔_𝑚1𝑉_𝑍1, 𝐼_𝑋1−=−𝜂₁𝑔_𝑚1𝑉_𝑍1, 𝐼_𝑋2+=𝛽₂𝑔_𝑚2𝑉_𝑍2, and 𝐼_𝑋2−=−𝜂₂𝑔_𝑚2𝑉_𝑍2. 𝛼_𝑝𝑖 represents the nonideal current transfer gain from the 𝑝 terminal to the 𝑍_𝑖 terminal of the MO-CCCDTA, 𝛼_𝑛𝑖 denotes the nonideal current transfer gain from the 𝑛 terminal to the 𝑍_𝑖 terminal of the MO-CCCDTA, 𝛽_𝑖 is the transconductance inaccuracy factor from the 𝑍_𝑖 terminal to the 𝑋_𝑖+ terminal of the MO-CCCDTA, and 𝜂_𝑖 is the transconductance inaccuracy factor from the 𝑍_𝑖 terminal to the 𝑋_𝑖− terminal of the MO-CCCDTA. Considering them, the modified CO and FO are given as CO∶𝛼_𝑝1𝛽₁𝑔_𝑚1𝑅₁=1,FO∶𝑓_𝑜=12𝜋𝛼_𝑝2𝛽₁𝜂₂𝑔_𝑚1𝑔_𝑚2𝐶₁𝐶₂. (6) The active and passive sensitivities are obtained as 𝑆^𝑓𝑜_{𝛼𝑝2,𝛽1,𝜂2}=𝑆^𝑓𝑜_{𝑔𝑚1,𝑔𝑚2}=−𝑆^𝑓𝑜_𝐶1,𝐶2=12. (7)

The active and passive sensitivities remain less than unity and hence the circuit exhibits a satisfactory sensitivity performance.

A study is next carried out on the effects of various parasitics of the MO-CCCDTA used in the proposed circuit. A practical MO-CCCDTA device can be modeled as ideal MO-CCCDTA with finite parasitic resistances and capacitances. Figure 3 shows the nonideal MO-CCCDTA model including its parasitic elements. The nonzero parasitic input impedances at terminals 𝑝 and 𝑛 of the MO-CCCDTA are represented by 𝑅_𝑝 and 𝑅_𝑛, respectively. The parasitic resistance 𝑅_𝑍𝑖(𝑖=1,2) and parasitic capacitance 𝐶_𝑍𝑖 appear between the high-impedance 𝑍_𝑖 terminals of the MO-CCCDTA and grounded. The parasitic resistance 𝑅_𝑋𝑖 and parasitic capacitance 𝐶_𝑋𝑖 appear between the high-impedance 𝑋_𝑖 terminals of the MO-CCCDTA and grounded. It is further noted that the proposed circuit employs external capacitors 𝐶₁ and 𝐶₂ parallel connecting to the terminals 𝑍₁ and 𝑍₂, respectively. As a result, the effects of the parasitic capacitances 𝐶_𝑍1 and 𝐶_𝑍2 can be absorbed, due to the fact that 𝐶₁≫𝐶_𝑍1, 𝐶_𝑋2− and 𝐶₂≫𝐶_𝑍2. To alleviate the effects of parasitic impedance at terminal 𝑋₁₊, the MO-CCCDTA should be designed to have a very low input parasitic resistance 𝑅_𝑝 at terminal 𝑝. In the ideal case, the value of input parasitic resistance at terminal 𝑝 is zero and terminal 𝑝 is virtually grounded. Thus, the parasitic impedance at terminal 𝑋₁₊ is connected between a virtual grounded resistance 𝑅_𝑝 and a true grounded impedance (𝑅_𝑋1+//𝐶_𝑋1+). This fact affects the operating frequency in the high frequency region. To reduce its effect, one possible solution is to make the operating frequency 𝜔_𝑜≪1/𝐶_𝑋1+(𝑅_𝑝//𝑅_𝑋1+). The parasitic capacitance 𝐶_𝑍2 can be absorbed in the external capacitance 𝐶₂, but the presence of parasitic resistance at terminal 𝑍₂ would change the type of the impedance, which should be of a purely capacitive character. To alleviate the effects of the parasitic resistance 𝑅_𝑍2, the operating frequency should be chosen such that 𝜔_𝑜≫1/(𝐶₂+𝐶_𝑍2)𝑅_𝑍2. In addition, the parasitic capacitance 𝐶_𝑋1− (or 𝐶_𝑋2+) and parasitic resistance 𝑅_𝑋1− (or 𝑅_𝑋2+) appear between the high-impedance 𝑋₁₋ (or 𝑋₂₊) terminal and ground. These parasitic components will affect the phase difference between the output currents. To reduce its effect, a possible solution is to make the operating frequency 𝜔_𝑜≪min{1/(𝐶_𝑋1−𝑅_𝑋1−),1/(𝐶_𝑋2+𝑅_𝑋2+)}. Therefore, the useful oscillation frequency range of the proposed oscillator is limited by the following conditions: 1𝐶₂+𝐶_𝑍2𝑅_𝑍2≪𝜔_𝑜1≪min𝐶_𝑋1+𝑅_𝑝//𝑅_𝑋1+,1𝐶_𝑋1−𝑅_𝑋1−,1𝐶_𝑋2+𝑅_𝑋2+. (8) Hence, the design procedure must satisfy the conditions 𝑅_𝑝 ≪𝑅_𝑋1+, 𝐶₁≫𝐶_𝑍1+𝐶_𝑋2−,   𝑅₁≫𝑅_𝑍1//𝑅_𝑋2−, and (8) to minimize the influence of the nonideal effects on the proposed circuit.

Figure 3 

Nonideal equivalent circuit model of the MO-CCCDTA.

4. Simulation Results

In order to verify the theoretical analysis, the proposed oscillator has been simulated using HSPICE program by using TSMC 0.18 µm CMOS process technology process parameters. The CMOS implementation of the MO-CCCDTA is shown in Figure 4 [25]. The aspect ratios (W/L) of the MOS transistors were taken as 8.75/0.18 for M1–M7; 17.5/0.18 for M8–M10; 10/0.5 for M11–M14; 25/0.8 for M15–M26; 8/0.8 for M27–M34; and 35/0.25 for M35–M38. It may be noted that some of the MOS transistors were used with large widths. This would occupy large area on the chip. The supply voltages are 𝑉_𝐷𝐷=−𝑉_𝑆𝑆=0.9 V; the biasing currents are 𝐼_𝐵1=𝐼_𝐵2=50 μA and 𝐼_𝐵3=𝐼_𝐵4 = 96.5 μA (𝑔_𝑚≅200 μS). 𝐼_𝐵1 and 𝐼_𝐵2 are the biasing currents for the device to perform the current differencing operation, while MO-CCCDTA transconductances are controlled by 𝐼_𝐵3 and 𝐼_𝐵4. The two capacitors in Figure 2 were set to be equal by 𝐶₁=𝐶₂=10 pF. 𝑅₁ was adjusted to 5.02 kΩ to start the oscillations. The theoretical oscillation frequency using this design was 3.183 MHz. The startup output waveforms for both the quadrature voltages and currents were shown in Figures 5 and 6, respectively. The steady state output waveforms for both the quadrature voltages and currents were shown in Figures 7 and 8, respectively. The frequency spectrums for both the quadrature voltages and currents were shown in Figures 9 and 10, respectively. From the simulation results, the oscillation frequency of 𝑓_𝑜≅3.17 MHz is obtained, which agrees very well with the theoretical analysis. The total harmonic distortions for voltage and current outputs 𝑉_𝑜1, 𝑉_𝑜2, 𝐼_𝑜1, and 𝐼_𝑜2 are 1.02%, 0.91%, 1.01%, and 0.87%, respectively. Figure 11 shows the variation of the transconductance value by changing 𝐼_𝐵4 from 5 to 150 μA. The electronic tuning of the 𝑉_𝑜1 oscillation frequency with the bias current 𝐼_𝐵4 was shown in Figure 12. These simulations results are close to the theoretical prediction and confirm the feasibility of the proposed configuration. In addition, the effect of mismatch errors of the current mirror on the performance of the proposed circuit is investigated by setting the value of 𝐼_𝐵4=96.5 μA with errors of −10%, −5%, +5%, and +10%, respectively. Simulation results show the slight oscillation frequencies which are approximately 3.09 MHz, 3.13 MHz, 3.21 MHz, and 3.25 MHz, respectively, all of which are less than ±3% in disagreement with the designed oscillation frequency of 𝑓_𝑜=3.183 MHz. Compared with the designed oscillation frequency, 𝑓_𝑜=3.183 MHz, the frequency deviation due to mismatch error of the current mirror is acceptable. Figure 13 shows the phases of quadrature voltage and current outputs. In Figure 13, the output files of Fourier analysis from simulation results were used for calculating the phase error. Figure 14 shows the total harmonic distortion values of voltage and current output signals. It can be seen that the total harmonic distortion values of output voltages and currents are less than 3.6%. The proposed sinusoidal oscillator has a simple topology and provides voltage-mode and current-mode operation with electronically tunable properties. The power dissipation is 1.427 mW.

Figure 4 

CMOS implementation of MO-CCCDTA [25].

Figure 5 

Transient amplitudes of the waveforms of 𝑉𝑜1 (blue) and 𝑉𝑜2 (red).

Figure 6 

Transient amplitudes of the waveforms of 𝐼𝑜1 (blue) and 𝐼𝑜2 (red).

Figure 7 

Simulated quadrature voltage output waves of 𝑉𝑜1 (blue) and 𝑉𝑜2 (red).

Figure 8 

Simulated quadrature current output waves of 𝐼𝑜1 (blue) and 𝐼𝑜2 (red).

Figure 9 

The simulated frequency spectrum of 𝑉𝑜1 (blue) and 𝑉𝑜2 (red).

Figure 10 

The simulated frequency spectrum of 𝐼𝑜1 (blue) and 𝐼𝑜2 (red).

Figure 11 

Variation of transconductance with bias current 𝐼𝐵4.

Figure 12 

Oscillation frequency against the bias current 𝐼𝐵4 of the circuit (o, simulated frequency, theoretical curves).

Figure 13 

Phase error as a function of oscillation frequency (blue: phase error versus 𝑉𝑜1 and 𝑉𝑜2 and red: phase error versus 𝐼𝑜1 and 𝐼𝑜2).

Figure 14 

Total harmonic distortion (THD) as a function of oscillation frequency (blue: 𝑉𝑜1; red: 𝑉𝑜2; pink: 𝐼𝑜1; and green: 𝐼𝑜2).

5. Conclusion

In this paper, a new quadrature oscillator circuit using a single MO-CCCDTA, two grounded capacitors, and one grounded resistor is presented. The oscillation condition and oscillation frequency of the proposed quadrature oscillator have the advantage of being independently controllable. Two high-output impedance sinusoid currents with a 90° phase difference are available in the proposed configuration. The use of all grounded passive elements makes the proposed circuit ideal for integrated circuit implementation. Both current-mode and voltage-mode quadrature signals can be simultaneously obtained in the proposed circuit. HSPICE simulation results have confirmed the workability of the circuit.

Conflict of Interests

The author declares that there is no conflict of interests regarding the publication of this paper.

Acknowledgments

The author is thankful to the anonymous reviewers for their suggestions to improve the paper. The author is also grateful to Professor Soliman A. Mahmoud, Editor, for recommending this paper.