Automatic tuning circuit

Automatic tuning circuit is an important component for continuous-time filters.

Usually, the RC time constant variation of more than 30% would be provided. Thus, the tuning circuit should be used to compensate deviation from process and temperature that affect filter accuracy. The frequency tuning is the most important approach in the automatic tuning circuit since the filter cutoff frequency determinates the system performance. However, the filter quality factor determinates the gain of the filter, and the Q tuning would be sometimes important especially in the narrow band applications. For the Gm-C implementation, we need the tuning circuit to modify the property of transconductance or loading capacitance. We should note that although the individual components are largely affected by the process variation, the ratio of the same components is still matched.

In the automatic tuning scheme, the filter characteristic is measured at first, and it would be compared with the desired value. Then, the corrective feedback signal is applied to reduce the error to zero. There are two kinds of the tuning architecture. One is the direct tuning architecture and the other is the indirect tuning architecture.

5.3.1 Direct tuning architecture

Figure 5.3. Indirect tuning scheme.

Fig. 5.2 shows the direct tuning architecture. The concept of direct tuning is to use the filter which processes actual signal. If continuous operation is required, the tuning algorithm should be able to avoid the effect of the filter transfer characteristic.

This architecture is similar with the adaptive tuning techniques. However, if the filter could operate under the sleep mode and be removed from the signal path at some times, the tuning can become simpler. This kind of tuning technique can be employed in the video filters, where tuning can be performed in the field fly-back interval [59].

5.3.2 Indirect tuning architecture

Since the tuning algorithm is very complicated, the indirect tuning architecture becomes popular and it is commonly used in circuit implementation. The indirect tuning can be referred to as the master-slave tuning. In other words, the filter is not directly tuned by using the filter output signal. The indirect tuning architecture is shown in Fig. 5.3. The slave filter that processes signal is left alone. The master block could be a transcontuctor or a filter. Any non-idealities of the master block would produce the same effects in the slave filter. If the characteristics of master block are corrected, the same information would be applied to the slave filter.

The first approach based on the integrator is discussed. Fig. 5.4 (a) shows the constant transconductance tuning. In the approach, the transconductance is set to the inverse of an external resistance. The circuit works as follows: if Gm of the

Figure 5.4. Frequency tuning circuit by using single transconductor. (a) Resistor based tuning. (b) Switch based tuning.

transconductor is small, the current through Rext is larger than the current supplied by the transconductor, and the difference between the two currents is integrated with the OPAMP and capacitor. Finally, the control voltage, V_ctrl, is increased until the same transconductance is obtained. Instead of the passive resistor, we can use the switch-capacitor circuit. Fig. 5.4 (b) shows the modified circuit, the equivalent resistance in Fig. 5.4 (a) is given by Rext = 1/(fclkCm). Thus, the transcontuctance is set to fclkCm. Under this condition, a precise tuning circuit can be achieved since Gm/CL is set to fclkCm/CL, and then the ratio of the capacitance can be hold. We should note that an additional low-pass filer has been added to remove the high frequency ripple voltage owing to the switched technology. However, some clock jitter would still leak into the slave filter through the control node. The other disadvantages of the approach for high speed filter are the required large capacitor ratio, which implies poor

Figure 5.5. Frequency tuning based on the VCO.

matching problem, and the high speed clock reference.

Another approach is based on the voltage controlled oscillator (VCO) technique.

The tuning scheme is shown in Fig 5.5. In the technique, two integrators are placed in a loop. Then, a phase lock loop (PLL) is used to achieve equal signal frequency between the external reference and the oscillator. In other words, the oscillator frequency of the VCO is equal to the external reference, and so does the filter pole frequency through the corrected voltage, Vctrl. The phase detector can be a simple XOR gate since only the phase variation should be detected. The problem of the VCO technique is the limited oscillation amplitude. Usually, a second-order harmonic oscillator is used, and the harmonic distortion of transconductor will shift the effective oscillation frequency. Thus, an amplitude regulation should be provided to make sure the high linearity operation of the transconductor. For best matching between the tuning circuitry and the slave filter, we should choose the equal value of reference signal frequency and cutoff frequency. However, the noise typically provides largest value at filter cutoff frequency, and therefore the signal leakage would largely degrade the filter dynamic range.

The voltage controlled filter (VCF) approach is another choice. The master block of the approach is composed by a second-order biquad low-pass filter, as shown in Fig. 5.6. Since a phase shift of 90^o can be obtained for the biquad, the multiplication of the phase should be equal to zero at locked condition. It means that the frequency dependent input to output phase characteristics of the reference are exploited to tune the circuit. For this reason, any offset in the phase comparator will result in a frequency tuning error. The performance, such as accuracy and speed, of the

Figure 5.6. Frequency tuning based on the VCF.

comparator should be maintained. In this approach, a high performance reference signal should also be required. The reason is that the harmonics would not behave the same phase shift as the fundamental frequency, and thus corrupt the result of phase comparison.

The above frequency tuning can be applied by tuning the transconductors continuously. The transconductor should be designed to have specified linearity over the tuning range, and much effort of the transconductor circuit should be taken. In addition to the tuning scheme performed in the analog domain, the digital frequency tuning scheme could be another issue. Through the use of programmable transistor or capacitor array, the linearity can be easily maintained at the expense of extra area and accuracy. In the programmable filter, the analog tuning circuit requires additional interface since the output is a voltage. Thus, the digital tuning circuit, which is composed by the counters and control logics, can be adopted for the programmable filter to control switches.

5.4 A 1 GHz equiripple low-pass filter with a high-speed automatic tuning