Active Inductor Based VCO

MOSFETs used in Active Inductor 6.2 Schematic Representation of Active Inductor

6.3 Active Inductor Based VCO

6.3.1 Barkhausen criteria

A small change In DC power supply or noise component in oscillator circuit can start oscillation and to maintain oscillation in circuit must satisfy Barkhausen’s criterion.

A

Vin

Vo

β

Figure 6.3 block diagram of oscillator

V_in =input voltage V_o =output voltage A = forward path gain

β = small fraction of output signal is feedback to input

 From the diagram we can conclude that, feedback voltage

 Barkhausen’s criterion states that,

The loop gain is equal to unity in absolute magnitude, that is,

1. : In this condition, feedback is greater than the input voltage Thus addition of input wave and feedback wave will result in larger amplitude wave and as oscillation goes on the amplitude will increase and this can be harmful for device.

2. : In this condition, feedback is less than the input voltage Thus addition of input wave and feedback wave will result in smaller amplitude wave and as oscillation goes on the amplitude will gradually decrease and oscillations will die out.

3. : In this condition, feedback equal to the input voltage Thus addition of input wave and feedback wave will result wave having amplitude of input and as

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oscillation goes on the amplitude will remain constant and hence a sustained oscillation is achieved.

 The phase shift around the loop is zero or an integer multiple of 2 . ... Complex value of is given by ...(6.10)

 In above expression imaginary part is zero because we assume phase shift zero or 360º now if phase shift isn’t zero then , which is not suitable condition for oscillation. For phase shift equal to 180º but input and feedback signal will be out of phase and they will cancel each other hence phase shift must be an integer multiple of 2 .

6.3.2 Conditions

 The oscillator must provide a large voltage gain to satisfy Barkhausen criteria in order to start oscillation.

 The total phase shift must be -180 degrees.

6.3.3 Choosing the configuration

Common source stage: When the source terminal of an MOS amplifier is common for both input and output, then the configuration is known as common source configuration. A common source configuration provides an output of -180 phase shift with a gain of -gmRD

where RD is the drain resistance at the output terminal.

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M R

_D

V

_in

V

_DD

V

_o

=-g

_m

R

_D

V

_in

Figure 6.4: Common source amplifier

The gain of the common source stage is given by A_v=-g_mR_D. So now neglecting the capacitances of the transistor, the voltage gain of the common-source amplification stage with a lossy LC tank load at the resonant frequency of the LC tank is given by A_v=-g_mR_p, where R_p is the parallel resistance of the tank. Now a phase delay of -180 is not practically possible, so two back to back common source amplifiers are required to provide the large phase shift. This back to back configuration, also called cross coupled transistor pair will act as negative resistor to provide large voltage gain by outperforming the ohmic loss of the LC tank.

V_b M7

M_neg M_neg

Figure 6.5: Cross coupled transistor pair

Here M₇ is operated in saturation region which will act as current source for biasing the cross- coupled transistor pair to control the g_m.

79 6.3.4 Choosing W/L ratios and applied voltages

Mneg: As the voltage gain of the oscillator must be sufficiently large and the voltage gain of the common source stage is –gmRD so W/L ratio needs to be chosen in such a way that the gm

is in its maximum value. The maximum width is 30μm in 90nm CMOS process and the minimum channel length is 100nm (though it is 90nm, but Virtuoso Cadence does not allow to use 90nm rather it offers to use a minimum of 100nm). So the W/L ratio for the M_neg is 30μm/100nm to achieve maximum gm. But the higher value of W/L or g_m has also a disadvantage. It increases the power consumed by the MOSFETs which reduces the output oscillation’s amplitude as well as the output power.

M₇: M₇ is used as biasing current source for controlling the resistance of the cross-coupled transistors. The more the W/L ratio for M₇ the more the value of I_ds as well as g_m . The higher value of I_ds will cause the higher value of gm for the M_neg. As g_m for M_neg has already been increased to its maximum value, so an optimum value of 30μm/100nm has been chosen with a multipliers of 3 for M₇.

Mcap: The MOS capacitors (M_cap) with a dc voltage source are employed to vary the oscillation frequency of the designed VCO. MOS with shorted drain and source terminal acts as capacitor which can be used as variable capacitor called MOS varactor . Here W/L ratio for the M_cap is 120nm/10μm with a multipliers of 15 and it provides a capacitance of 18.096fF.

Supply voltage, biasing voltage and control voltage: Supply voltage V_DD=1.8 V is used. A biasing voltage of V_b=0.5 V is used to operate the MOS which acts as current source in saturation voltage. V_control=0V to 0.8V is used to tune the capacitances of the M_cap as well as the oscillation frequency.

Table 6.2 summarizes the VCO’s network

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Table 6.2: Summary of W/L ratios & applied voltages used in proposed VCO‟s network

The next section illustrates the schematic representation of the proposed active inductor based VCO . The dotted lines represents the active inductor’s section, M_negs are cross coupled transistor pair. M_caps are MOS capacitors and M₇ at the tail of the network works as biasing current sources for M_neg.

MOS Width(μm) Length(nm)

M1 27 200

M2 15 100

M3 30 350

M4 10 200

M5 22 200

M6 5 200

M7 30 300 ( multipliers=3)

Mneg 30 100

M_cap ^0.120 10 ( multipliers=15)

Supply voltage ,V_DD=1 V Biasing voltage Vb=0.5 V Control voltage, V_control=0 to 0.8 V

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