A P P L I C AT I O N S
M O B I L E CO M M U N I C AT I O N S
Fundamentals of oscillators for the microwave range
Foto: SES/ASTRA
Maximum stability
The author,
GERHARD
LOHNINGER,
Dipl.-Ing., is project
manager for
silicon MMICs and
responsible for
product support
for fourth-generation bipolar transistors (SIEGET).
He is also responsible for product
definition of
discrete silicon RF
semiconductors.
Oscillators are important components of electronic circuits throughout the frequency spectrum. They
may be divided into fixed-frequency oscillators and tunable voltagecontrolled oscillators (VCOs). The
former are commonly used to drive
mixers or as transmitters with or
without an amplifier output stage.
Prime examples are satellite reception in the ASTRA band, where a
10 GHz local oscillator down-converts the carrier to an IF of 0.95 to
1.75 GHz, or a 2.45 GHz Doppler
radar module whose core is a multilayer epoxy board containing a
stabilized oscillator. VCOs are
mainly used in phase-locked loop
(PLL) systems, which make different frequency settings possible
within a defined frequency band.
Examples are VCO modules in mobile phones or TV and radio receivers. Although the basics of both
oscillator types are the same, this
article is confined to the fixed-frequency variety.
(1/98.3.1)
In communications, instrumentation and computer applications, stable oscillators for
signal generation and control
are essential to the functionality
and performance of countless
electronic circuits,modules and
systems. Silicon bipolar transistors BFP 405, BFP 420 and
BFR 92P, and bias controller
BCR 400 are key components of
oscillators for these vital functions.
Feedback or negative resistance
Oscillators can be described as
circuits based on the principle of
feedback or negative resistance.
Feedback oscillators operate with
active components, i.e. transistors,
whereas negative resistance oscillators use Gunn, IMPATT (impact
ionization and avalanche transit
time) or BARRIT (barrier injection
transit time) diodes. The negative
resistance and thus the application
potential of these components as
active oscillators can be derived
from their voltage-current characteristic. The noise signal Ein acts as
the input signal to the feedback
circuit. It is distributed over various
components. The output signal E0 is
calculated from the relationship
This yields
the phase along the loop must be a
multiple of the angle ϕ, i.e. 2πn.
When the signal increases due to
excitation by noise, nonlinear effects subsequently reduce the loop
gain until the stationary condition
GD(e)H = 1 and phase ϕ = 2πn are
satisfied.
Another method of calculating the
requirement for oscillation is provided by the negative resistance
model. Here the resistance -RD must
represent a defined variable to
excite an oscillation. The noise voltage Ein is not present until the
system’s operating voltage is
applied and therefore has the
characteristic of a conditional jump.
The resistance -RD and the capacitance C are assigned to the active
part (device), while the inductance
L and resistance RL belong to the
circuit load. With the aid of a
Laplace transform, the temporal
variation of E0 as a function of Ein in
the presence of a conditional jump
can be calculated as follows:
To generate an oscillation, the loop
gain must be greater than 1 when
the operating voltage is applied, and
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Components 1/98
A P P L I C AT I O N S
M O B I L E CO M M U N I C AT I O N S
where Ein (t) in the time domain ⇔
Ein (s)/s in the frequency domain,
and L.di(t)/dt ⇔ L.s.I(s), where
Feedback and negative resistance circuits
The time function E0 can be determined from the image function by
transformation into the original
function with the aid of the conversion formulas as follows:
(1/98.3.2)
I(s)/ Cs and R.i(t) ⇔ R.I(s).
The feedback structure (left) consists of a linear amplifier of gain G, a nonlinear component D(e)
and a feedback gain H.The equivalent circuit diagram of a negative resistance oscillator is shown
on the right.
Colpitts oscillator
Given that
,
For inductive
loads this
configuration
produces a
Colpitts oscillator.The steepness of the
slope gm
depends on the
operating
current of the
transistor.
This yields the voltage E0 in the
time domain as follows:
(1/98.3.3)
corresponds in the
time domain to
Smith diagram
Components 1/98
Load impedance
Z(ω) (load line)
and impedance
Z(A) (device line)
of a typical circuit
in the Smith
diagram.
Small signal
(1/98.3.4)
So if the magnitude of resistance
-RD is greater than RL, an oscillation
will start to develop from the noise.
If a quality term (Q = ω0L/RL) is
introduced, a smaller frequency
shift occurs from the beginning of
the oscillation up to the stationary
condition at the frequency ω0. If the
definitions Z(A) = -ZD = RD-jXD and
Z(ω) = ZL = RL+jXL apply to the
impedances, then Z(A) = Z(ω) must
apply to the stationary oscillator
condition, i.e. RL = RD and XD = XL.
The output voltage E0 is then Ein
sin(ω0t) / Q if nonlinear effects are
neglected.
Both types of calculation, negative
resistance and feedback, may be
used for feedback oscillators. If a
bipolar transistor is simulated by a
simple equivalent circuit and recalculated with the aid of the complex
calculation, the resistance RD is
The following apply to
point P2:
Z(A) = R(A) - jX(A)
= 25Ω + j 10 Ω
ZD =-Z(A) = -25Ω - j 10 Ω
Z(A) = Z(W)
In the stationary case
Z(ω) = 25 Ω + j 10 Ω
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A P P L I C AT I O N S
M O B I L E CO M M U N I C AT I O N S
(1/98.3.5)
Amplitude and phase conditions
obtained as follows:
RD = -gm/ω2C1·C2 (Colpitts
oscillator)
Operating point and load
impedance
Assuming that variation of the
impedance Z(A) with frequency is
obtained by adjusting the oscillator’s tuning screw, there will be a
stable, low-noise operating point at
P1, as shown in the Smith diagram.
The conditions for this are:
1. The angle ϕ (phi) must lie between 0 and 180°. The angle ϕ is
defined as the tangent at Z(A) [at
point P1 pointing away from the
small-signal impedance] turning
clockwise toward the tangent at
Z(ω) [at point P1 in
Oscillators are used for
the direction of rising
triggering mixer components, as
transmitters in satellite communi- frequency].
cations and in other demanding 2. Minimum phase
applications. They can be intenoise occurs when
grated into circuits with feedback
ϕ = 90°.
or negative resistance. Fixedfrequency oscillators must satisfy 3. When the operating
special conditions in each circuit voltage is applied, the
type.
stable operating point
is the one that first
describes an angle ϕ from 0 to 180°
starting from small-signal operation.
At an operating frequency f B of
9.35 GHz (point P2), for example,
this means that a load impedance is
required with a real component of
25 Ω and an inductive component
of 0.17 nH. This guarantees a
16
The load
impedance Z(ω)
is the critical
parameter of a
stable oscillator
function.The two
reflection factors
must satisfy
defined
conditions.
stable, low-noise operating point.
If the oscillator is operated along
the curve Z(A) with the relevant
operating points P3, P4 and P5,
then point P4 is set after the
operating voltage has been applied.
P5 is not a stable operating point
because the angle ϕ is greater than
180°.
If the oscillator’s operating voltage
is applied (P1) and the distance between resonator and tuning screw
reduced, then point P2 is reached
first, followed by P3 up to P6. No
stable point exists there, and a
frequency jump to P7 occurs. In the
reverse case, P7 is a stable operating point starting at a high
frequency. As the distance between
tuning screw and resonator increases, the region between P4 and
P5 is reached, where the frequency
jumps between P3 and P2 (hysteresis). Resonant load curves must
therefore be avoided in the vicinity
of the operating point, as the
oscillation may become unstable
if the temperature fluctuates
(Z(A)changes).
A rule of thumb for optimum load
impedance is
R(A) ≅ R(A0)/2.
where Z(A0) represents the input
impedance for the oscillator in
small-signal operation, i.e. at the
first moment that the operating
voltage is activated. A derivative of
these relationships shows that the
oscillator delivers more or less its
maximum power.
As soon as a first design is available, however, it is much more
efficient to perform measurements
with a tuner (load pulling). This is
an RF instrument with which practically all the impedances of a
Smith chart – except for very high
or low values – can be implemented. Various measurement and
calibration procedures make it possible to measure the impedance set
on the tuner at a particular oscillator
output power. Measurement can
be simplified by using automatic
tuning systems with suitable programming.
A somewhat different approach is
of particular interest for VCOs and
serial feedback oscillators. To meet
the oscillation requirements, the
reflection factors ΓD and ΓL must
correlate as follows:
ΓD ·ΓL = 1
The equation can therefore be resolved into two partial conditions:
1. Amplitude condition:
|ΓD| · |ΓL| ≥1
2. Phase condition:
ϕ (ΓD) + ϕ (ΓL) = 2πn
(where n = 0, 1, 2,...)
This means that the oscillation
conditions can be checked at every
oscillator port and the circuit
properties optimized to initiate
oscillations.
The second part of this article
covering applications with silicon
bipolar RF transistors and the BCR
400 bias controller will appear in
the next issue of Components.
Check #1-98-3 (HL)
on Reader Service Card
gerhard.lohninger@hl.siemens.de
Components 1/98