Analysis of Voltage-Controlled Oscillator

The voltage-controlled oscillator is used to provide clock signal at the certain frequency for the charge pump. From the discussion on the section 5.3.1, the design considerations of the voltage-controlled oscillator are the following: the operating frequency requires exceeding the range of 400 kHz to 1.6 MHz, and the center frequency requires setting to 800 kHz.

The kernel of the voltage-controlled oscillator used in this work is a source coupled multivibrator, which represents the CMOS version of a well-known bipolar emitter-coupled multivibrator [46], [50]. This circuit topology has been widely used in applications involving waveform generation, such as voltage-controlled oscillators for phase-locked loops (PLLs), because of the low count of active components. The conceptual representation of the basic operation is shown in Fig. 5.10(a) and (b) [47]-[49]. Assume the currents I1 and I2 are equal to ID, and the circuit is already at one of its two stable states, for which transistor M1 is ON. As a consequence, the voltage at node X is fixed as

( ) ( )

X DD 1 1 2 DD 1 2 D

V =V −R I +I =V −R I (5.4)

Complementary, transistor M2 is OFF, and current I2 directly discharging the timing capacitor Ctime decreases Y node voltage. Therefore, M2 will maintain its OFF state until voltage Vgs2 is large enough for conduction. As a result, the gate of transistor M1, which was initially at VDD

due to the lack of current flowing through R2, changes to a lower voltage given as

( ) ( )

g,M1 DD 2 1 2 DD 2 2 D

V =V −R I +I =V −R I (5.5)

which toggles its state. As a consequence M1 turns off and the process repeats again. Note

that the effect of asymmetrical current I1 and I2 results in different slopes of capacitor voltage charge, therefore providing a duty cycle different from 50%.

(a) (b)

Fig. 5.10 Conceptual representation of the basic source coupled multivibrator operation.

Fig. 5.11(a) shows a schematic of a source coupled multivibrator, and the simplified schematic shown in Fig. 5.11(b) is helpful in illustrating the oscillator operation and determining the oscillator frequency. Cross-coupled transistors M1 and M2 operate as switches and provide the oscillation feedback. The discharge transistors M5 and M6 behave as two current sources sinking a current ID. The charging currents for each branch of the oscillator are supplied by M3 and M4, which pull the output to VDD. If M1 is on and M2 is off, the drain of M2 is pulled to VDD by M4 and this is the high voltage level of VO. Since the gate of M1 is at VDD, the source and drain of M1 are approximately (VDD – Vtn,M1) and this is the low voltage level of V . In addition, _O V referred to the gate voltage of M2 is held at the _O voltage (VDD – Vtn,M1) through M1 until M2 turns on and M1 turns off. Initially, at the moment when M1 turns on and M2 turns off, point Y tracing the drain voltage of M2 is VDD. Afterward the current ID through Ctime causes point Y to discharge down toward ground. When point Y gets down to (VDD – Vtn,M1 – Vtn,M2), M2 turns on and M1 turns off. As a consequence VO gets down to its low voltage level (VDD – Vtn,M2) and V pulls to its high voltage level V_O DD.

The wave forms at the points X, Y, VO, and V are shown in Fig. 5.12 for continuous time _O operation. Assuming that V_tn,M1=V_tn,M2 =V , V_tn O and V are out of phase with the same _O voltage swing range from (VDD – Vtn) to VDD. Since the oscillator output signals are not yet digital, the oscillator requires a buffer, possibly an inverter or self-biased differential amplifier to restore CMOS logic levels.

(a) (b)

Fig. 5.11 (a) Schematic of a source coupled multivibrator. (b) Simplified schematic of source coupled multivibrator, where M1 is on and M2 is off.

Fig. 5.12 Voltage waveforms of the source coupled multivibrator.

Furthermore, the voltage at point Y changed an amount of (Vtn,M1 + Vtn,M2) before switching took place. The time takes point Y to change (Vtn,M1 + Vtn,M2) is given by

(

)

V V C

t I

∆ = + (5.6)

Since the circuit is symmetrical, two of these discharging times are needed for each cycle of the oscillator. When V_tn,M1 =V_tn,M2 =V , the frequency of oscillation is given as _tn

^D

Briefly, the oscillation frequency of the source coupled multivibrator is proportional to the value of the charging current and inversely proportional to the value of the floating timing capacitor Ctime. In other words, the oscillation frequency is determined by the charging and discharging slopes of Ctime. Referring to Fig. 5.11, the total current supplied to the oscillator is 2ID, but only one-half of the total current contributes to the charging current of Ctime. The rest current does not affect the operating speed and thus it becomes a waste in terms of the power consumption. However, its current operation scheme provides a broad frequency control range.

The direct implementation of the previous voltage-controlled oscillator at transistor level is depicted in Fig. 5.13. The whole circuit is realized by three functional blocks: the main source coupled multivibrator determining the oscillation frequency, the input bias circuit supporting a control bias voltage to change the charging current of Ctime, and the output buffer providing the logic operation with a large driving ability. Fig. 5.14 shows the simulation results of the output frequency with different input control voltage Vc, where Ctime = 3 pF and VDD = 1.5 V.

The operating frequency range is observed from 60 kHz to 4.2 MHz, which is larger than the required range specified in section 5.3.1 (400 kHz to 1.6 MHz). The center frequency is obtained at 800 kHz while Vc is 1.0 V. A limited adjustable range of Vc is observed from 0.6 V to 1.5 V because a small supply voltage VDD is used.

Fig. 5.13 Overall schematic of the voltage-controlled oscillator circuit.

Fig. 5.14 Oscillation frequency (fs) versus input control voltage (Vc).