Frequency tuning loop for VCOs

FREQUENCY TUNING LOOP FOR VCOS B. Linares-Barranco’, A. Rodriguez-Vbquez2, E. Shchez-Sinencio’ and J. L. Huertas2 ’ Department of Electrical Engineering Texas A&M University, College Station, TX 77843-USA Dpto. de Diseiio Analbgico, Centro Nacional de Microelectrbnica, 41012-Sevilla, Spain Abstract-For a Voltage Controlled Oscillator (VCO) the oscillating frequency is controlled by an external input. The relationship between the oscillating frequency and the input control voltage is, in most cases, expected to be linear and independent of parasitics, process parameters, temperature, and other non-idealitites. In this paper we introduce a frequency tuning circuit for VCOs so t4at the Anal relationship between oscillating frequency and input control voltage is Axed and independent of the previous mentioned non-idealities. This tuning loop is applied to an OTA-C sinusoidal VCO. Such an oscillator has an output frequency-input voltage relationship that depends on temperature, process parameters, and even amplitude of the oscillations. It is shown that by adding the tuning loop all these non-ideal dependences will be minimized. I. INTRODUCTION Voltage Controlled Oscillators are key components in many signal processing and communication systems [l-31, and are also used for the tuning of monolithic filters [4-91. They alsomay be used for instrumentation applications [2]. In many cases it is necessary that the relationship between the actual oscillating frequency of the VCO and its input control voltage is very precise and does not change with temperature, process parameters or parasitics. Consider a certain VCO (sinusoidal, triangular, or square wave,) that has an “uncontrolled” input voltageoutput frequency characteristics. We will show that by adding the frequency tuning loop described in this paper the input voltageoutput frequency relationship can be made very linear and completely independent of secondary parameters (temperature, amplitude, parasitics, and process parameters) within the tuning range of the original VCO. The tuning loop proposed in this paper is valid for any type of VCO. We are going to verify its operation by applying it to an OTA-C sinusoidal VCO [lo]. Sinusoidal OTA-C VCOs have a nonlinear input voltageoutput frequency relationship that depends on process parameters, temperature, parasitic components and even amplitude of the oscillations. By adding the proposed tuning loop we will show that this relationship will become linear and independent of the previously mentioned parameters. 11. THE FREQUENCY TUNING LOOP Figure 1 shows the basic structure of the frequency tuning loop [11,12]. vco “OU? I Squarewave Converter Frequency Divider by N (Optional) Fig. 1. Block Diagram of Frequency Control Loop. The output of the oscillator (if not square) is converted to a square wave, divided by N (optional) and applied to a Frequency-twVoltage (FTV) converter. Usually the maximum operating frequency of an oscillator is higher than the maximum possible frequency in a Frequency-to-Voltage Convertor. For this reason the inclusion of the frequency divider in Fig. 1 is many times mandatory. As we will see in the next section, the FTV converter is a device such that if fin is the frequency of its input signal, its output voltage will be given by fin fREF Vz = n VBIAS- Where n is a positive integer, VBlAS is a reference voltage and fREF the frequency of a reference square wave CH 30064/91/0000 - 2617 $1.00 C IEEE signal (like a crystal oscillator). If f is the output frequency of the VCO and a frequency divider is used with a rate N, then fin = f/N. If p-' is the time constant of the integrator, its output voltage will be given by: Vr = ~(vco - vz) (2) On the other hand, for a CMOS OTA-C sinusoidal oscillator we have 1131, (3) K f = re = -(V -v ih) 2* c 2TC where K and Vth are given by the topology and transistor geometries of the OTAs used as well as by the process parameters. Solving equations (l), (2) and (3) yields, Vco - VBIAS- NfREF which has a stable stationary point (!$ < 0) characterized by N Vco f = fREF- ~VBIAS (5) The relation between f (output frequency) and V,, (input voltage) is shown in Fig. 2. Note that it is linear and it depends only on fREF, VBIAS, n and N. In the next Section we will give the implementation details of the FTV converter, which is the key component of the frequency tuning loop. ,f Fig. 2. Fkequency vs control voltage relationship for V,, with frequency tuning loop. 111. The FTV Converter Consider the circuiteof Fig. 3. It contains a monostable that produces a pulse of duration to = 1 During this pulse, capacitor C is charged by a current go (~~VBIAS - vz). The rest of the time it is discharged by goV,. The waveform that results at the capacitor u(t) is shown in Fig. 4. For each cycle of u(t), Vz(t) is the peak value of u(t) of the previous cycle. Two consecutive peak values are related by 2fREF ' V,(t+nT) = V,(t)-g"Vz(NT-to)+g"(2nv~~~s-vz)t, where T = 1/ f. If f is constant and the FTV converter C C (6) reaches its steady state, then Vz(t + NT) = Vz(t), i.e., A stability condition for the steady state can be obtained by writing (6) in the Z-domain and making the poles to be inside the unity circle. The resulting condition is [E], (8) Ngo f'2C A convenient IC implementation for this FTV converter is shown in Fig. 5. To improve the time response, the switch of Fig. 3 has been replaced by a differential pair and current mirrors. The current sources are implemented with linearized OTAs. to = tr, --I+ MONOSTABLE N I 1 4 Detector Ujt, Peak &- - - Fig. 3. Fkequency-to-Voltage Converter t- u(t) Fig. 4. Time waveforms of U( f) inside the FTV Converter, and of Vx(t), its output. tsv 1. --cHc Ju-l- V, ItJ Fig. 5. CMOS Circuit Implementation of FTV Converter 2618 The monostable has to provide a pulse of duration to = 1/2fREF. such a circuit is shown in Fig. 6. The duration of the output pulse to is given by the time it takes to charge capacitor CI from OV to VREF by the current IREF. VREF is given by the voltage to which Cz is charged, starting at OV by a current IREF during a time to = 1/2fREF. Therefore, if the two circuits enclosed by broken lines in Fig. 6 are perfectly matched, the duration of the monostable output pulse will be to = 1/2fREF, independent of IREF and cl = cz = c. If there is a mismatch between the two circuits the width of the monostable output pulse will not be equal to half the period of reference signal REF. However, besides this, the operation and characteristics of the tuning loop still remain basically invariant. r--------------- _L ICIl I1 I- - - a ____-- M.tChcd ChUit. -rc--c I. Fig. 6. Block Diagram of Monostable with Output Pulse Width Controlled by an External Square Wave Signal of Precise Frequency. IV. EXPERIMENTAL RESULTS In order to test theoproposed frequency tuning loop strategy we used a sinusoidal OTA-C oscillator [10,12]. Its frequency dependence is shown in Fig. 7. Note that the relationship between output frequency and input voltage (Bias Voltage) is nonlinear and changes with the amplitude of the oscillations. A discrete frequency tuning loop was implemented around the previous CMOS OTA-C oscillator. Since the output frequency gdes over 13MHz, a fast comparator (CM710C) was used to convert the sinusoid to a square wave signal. For the monostable a conventional 555 timer was used. In this case, the width of its output pulse is not controlled by an external frequency reference, but by a precise RC constant. Also, since this circuit has very bad time response (propagation times are around lOOns the output of the oscillator had to be divided by 32. The resulting output frequency-input voltage relationship of the VCO with frequency tuning loop is shown in Fig. 8. This characteristic is the same for different values of the oscillating amplitudes, for dif- .O Bias Vdtog. (volts) Fig. 7. Frequency vs Bias Voltage for sinusoidal OTA-C Oscillator without frequency tuning loop. ferent temperatures and for different IC chips. At this time we do not have available a complete IC prototype to quantify the degree of linearity, which is highly dependent on the implementation. 14.0' 13.0. 12.0, 11.0 CI Y E" '"5 8. f ;:5 1 6.0 5.0- 4.0. 3.0. 2.0 + 1:O 1:1 1:2 1.3 114 115 1.6 1.7 Froquoncy Control V&ap (Vdb) Fig. 8. Measured Oscillation Frequency vs Frequency Control Voltage of VCO with Frequency Tuning Loop. V. CONCLUSIONS A frequency tuning loop for VCOs is presented that compensates for temperature, process parameters, amplitude, and parasitics influence in the original output frequency-input volt age relationship. This tuning loop can be applied to any type of VCO. Its viability has been demonstrated, by applying it to a sinusoidal OTA-C VCO. The tuning loop was constructed using a breadboard prototype, but it can be integrated together with the oscillator in the same IC die [14]. 2619 VI. REFERENCES [ 11 K.K. Clarke and D.J. Hess, “Communication Circuits: Analysis and Design”, Addison Wesley 1978. 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