Oscillators2_w05

8/14/2019 Oscillators2_w05

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Note: The buffer amplifier is untuned. Thus, we need to avoid reduced conduction angle

modes such as Class AB or Class B. There is no low impedance termination for even-order harmonic frequencies. Harmonic termination is needed to form the half sine wave

current waveform for Class B. A push-pull design with appropriate transformer could be

used if Class B is desired.

We must work within the limitations of the device chosen for the buffer.

IC,max

BV,CEO

Tmax

These can typically be found on the data sheet. A safe design does not run all the way to

the limits of the device, so a reasonable margin needs to be provided. It may not be wiseto exceed 75% of the recommended maximum values.

For the Class A buffer amplifier, the peak values of voltage and current are:

VCE, max = VCC + ICQ RL

IC, max = 2 ICQ

Lets design a buffer.

Specs: 7 dBm output power (5 mW; 0.71V in 50 ohms); Source impedance = 100 ohms.

Voltage output from oscillator = 0.5V.

The device has: BVCEO = 12V; IC, max = 100 mA

1. Determine ICQ.

We start with RL = 50 ohms.

Po = ICQ2

RL/2 = 0.005 W ICQ = 14.2 mA.

This gives us a maximum current of 28.4 mA, well within the limits of the device.

2. Determine RE.

This will be determined by the gain required.

Av= 0.71/0.5 = 1.42= Lm L

e E

g Rr R

=

+


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gm = 0.55; re = 1.8 ohms. So, RE = (RL/Av) re = 33 ohms.

Check the input resistance: RB||RE (+1) >> RS. Make sure the bias resistors (RB) dontload down the oscillator or reduce the input amplitude significantly.

3. Determine VCC,min, VCC,max. This is the range of acceptable power supply voltageswhich avoid clipping and breakdown.

VCC, min = VCE,sat + ICQ (RL + 2RE) = 2.1 V

VCC, max = 0.75 BV,CEO ICQ RL = 8.3 V

4. Check for temperature rise

Worst-case Power Dissipation = PD = VCC ICQ for Class A

Choose VCC = 5V. PD = 71 mW. (This will drop to approximately 66 mW at fulloutput, but you must design for the worst case where the oscillator may fail to produce an

output.)

Tmax = RTH PD + Tambient

where RTH is the Thermal Resistance (degree C/Watt)

Maximum temperature is usually 150 C. If you exceed this, then you must reduce VCC or

ICQ.

5. Stability. Finally, you must check for stability over a wide range of frequencies. Usethe S parameter simulation mode in ADS and plot k and mag delta vs frequency. If there

are potential instabilities, you must deal with them using techniques that were employed

with the power amplifier designs last quarter.


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Resonator Design for Low Phase Noise Oscillators

Phase noise can be estimated by a simplified version of Leesons equation:

202

2 sig u

kTFlog

P Q

10

(1)

This is a noise power (single sideband) to carrier power ratio normalized to a 1 Hz

bandwidth. Units are dBc/Hz.

We saw that Vres = 2 IBIAS Rp is an approximation of the voltage across the resonator for

the Colpitts oscillator.

Qu = Rp/Xp = Bp/Gp for a simple parallel LRC resonant circuit.

So, how can we modify the circuit to improve the noise to carrier ratio? From theequation (1), increasing Psig and Qu would help. The former increases carrier power,

whereas the latter reduces noise generated by losses in the resonator and also does a

better job of bandpass filtering the noise. We increase signal power by increasing voltageor current.

2 2 sig res BIAS p P V or I or R

2

Inductor:

Lets assume that the inductor limits the Qu. This is typically true at frequencies below10 GHz or so. How can we increase Qu or Rp at a given frequency?

Qu = L/Rs for a series LR.

S. Long January 19, 2005 1


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For a coil inductor (whether on a magnetic core or in air) with N turns, we can assume

that the series resistance increases in proportion with length of the wire, therefore with N.The inductance will increase in proportion to N

2. Thus, Qu increases in proportion to N.

What about Rp?

2 2

ps s

X L

R

2

R R

= = and thus should increase as N3

.

This is an ideal version and in reality may not scale as favorably. Skin effect will causeRs to increase with frequency for example. Also, if we consider a spiral inductor on an

RFIC, the inner turns have less area than the outer ones. They contribute less inductance

per turn than a solenoidal coil, so the scaling is not obvious and requires E/M simulationto determine Qu and Rp.

Another consideration is what Q definition should be used? There are several:

0

0

sQ L / R

Energy StoredQ

Power Dissipated

dQ

d

=

=

=

=

(2abc)

Analysis of oscillators has shown that the last definition, the phase slope with frequency,correlates best with phase noise performance. While these definitions may predict the

same Q for simple resonators (series or parallel RLC), they do not agree very well with

more complicated topologies or with transmission line resonators.

How can we improve Psig? Any increase in IBIAS or Vres will help, but our device may

begin to clip or breakdown. There are limits to how much voltage and current a device

can handle safely. Simply increasing Rp will increase Vres, but may reach these limits inthe device. So, a better approach is to modify the topology so that more power can be put

into the resonator without exceeding the limits of the transistor. There are many such

attempts in the literature of oscillators to do this, but two approaches will be brieflyreviewed here.

1. Tapped inductor.2. Clapp oscillator.



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1. Tapped Inductor Oscillator.Vres

N

1

IBIAS

N

1

IBIAS

VC

C1

C2

Here we see a modified version of the Colpitts. The tapped capacitor provides the

feedback as before, but now there is a tapped inductor, an autotransformer with turnsratio N.

This has the effect of reducing the collector voltage, VC = Vres/(N+1). It also reduces the load resistance at the collector. RL = Rp/(N+1)

2.

If the tapping ratio was 1:1, then VC = Vres/2 and RL = Rp/4. Thus, we can now increaseIBIAS by a factor of 4, increasing the Psig by 16 times, without increasing the voltage

swing at the collector. Of course, the noise contribution of the transistor generally also

increases with IBIAS, so the net result is a 4 times improvement in phase noise to carrierratio (6 dB). Scaling to higher N values may be beneficial, but it depends on how Rp

scales with N. This can only be determined accurately by measurement or E/M

simulation of the inductor.



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2. Clapp Oscillator

CC

C2

C1

L

RS

Z(j)

RE

IBIAS

VCC

CC

C2

C1

L

RS

Z(j)

RE

IBIAS

VCC

In this case, the resonator is modified by adding a capacitor CC in series with the inductorL. This allows the inductance to be increased (Qu, Rp higher) from its Colpitts value, L0.

To keep the resonant frequency the same, the imaginary part of the impedance of the

series LRC resonator must be the same as that of L0. If we increase the inductance by afactor P

1,

( )0 01/ C j L P C j L = . (3)

From this, we can determine CC:

20

1

( 1CC

L P=

). (4)

To determine what effect the series RLC resonator has on the load presented to the

collector, RL, we must first find Z(j), then Y(j), then determine RL from 1/Re{Y(j)}.

Define (5)0u sQ L / R PL / = =

sR

1 W. Hayward, Introduction to Radio Frequency Design, Ch. 7, American Radio Relay League, 1994.



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uQ is the unloaded Q and sR

corresponds to the series resistance of the Clapp inductor,

L = PL0.

Eliminating CC, we get for Z:

( )( )00

0( ) 1/u

C

u u

L P jQPL Z j j PL C

Q Q

+= + =

(6)

Y = 1/Z, so

( )0

1/

Re ( )

uL u

u

QPR L

Y j Q P

= = + =

0L Q P (7)

because P/Qu


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Observation #2: The loading that the collector sees with the Clapp resonator is reduced

by a factor of Pbelow the Colpitts. Therefore, IBIAS can be increased by a factor of

P while maintaining the same collector voltage.

Observation #3: How much more energy is stored in the Clapp resonator than in the

Colpitts?

Vres is increased by the presence of a third capacitor, CC, in series with C1 and C23.

Energy = CTOTAL V2res

CC

C2

C1

L

RS

Z(j)

RE

IBIAS

VCC

CC

C2

C1

L

RS

Z(j)

RE

IBIAS

VCC

Vres

Let the series capacitance of C1 and C2 be represented by C12.

1 212

1 2

C CC

C C=

+

Then,

12 1 2

12 1 2 2 1

C CTOTAL

C C

C C C C C

C C C C C C C C C = =+ + + C

122

Cres

C

C CV V

C+ =

3 T. H. Lee, Design of CMOS Radio Frequency Integrated Circuits, Cambridge, 1998.



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Then,

21212 2

1

2

C

C

C C Energy C V

C

+=

If we then increase IBIAS by a factor of P, V2 remains the same as in the unmodifiedColpitts case, but the energy has increased by the factor

12 C

C

C C

C

+

as does the Psig.



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Oscillators2_w05