# The mysteries of RF amplifier stability...

B

#### billcalley

Jan 1, 1970
0
Hi All,

I'm having a very hard time understanding the full picture on
amplifier stability, even if I am an engineer. For instance, if we
select a transistor that is unconditionally stable at our frequency
band of interest -- let's say from 900MHz to 1000MHz -- but the
transistor is only conditionally stable at all other frequencies: So,
we bias, match, and resistively stabilize the transistor so that we
finally see, in the linear simulator, that K is greater than 1, and B1
is greater than 0. This should indicate that we now know that the
amplifier will not oscillate under any input/output impedance
conditions. But what happens when you place a filter at the input or
output port of our newly stabilized amplifier? Since the stopbands of
the filter are anything *but* 50 ohms when the amplifier is looking
out-of-band, wouldn't there still be a chance that this
"unconditionally stable" amplifier could oscillate, since it is only
based on a conditionally stable transistor?

Thanks!

-Bill

D

#### Dave (from the UK)

Jan 1, 1970
0
billcalley said:
Hi All,

I'm having a very hard time understanding the full picture on
amplifier stability, even if I am an engineer. For instance, if we
select a transistor that is unconditionally stable at our frequency
band of interest -- let's say from 900MHz to 1000MHz -- but the
transistor is only conditionally stable at all other frequencies: So,
we bias, match, and resistively stabilize the transistor so that we
finally see, in the linear simulator, that K is greater than 1, and B1
is greater than 0. This should indicate that we now know that the
amplifier will not oscillate under any input/output impedance
conditions. But what happens when you place a filter at the input or
output port of our newly stabilized amplifier? Since the stopbands of
the filter are anything *but* 50 ohms when the amplifier is looking
out-of-band, wouldn't there still be a chance that this
"unconditionally stable" amplifier could oscillate, since it is only
based on a conditionally stable transistor?

Thanks!

-Bill
An unconditionally stable transistor would be of no use other than as a
door stop, (at least in any definition of unconditionally stable I know
of). Perhaps you can define what you mean by "unconditionally stable
transistor".

You can always take a transistor and turn it into an oscillator if you
try to.

An unconditionally stable amplifier is a different beast all together.
That is a collect of parts. In theory it will not oscillate no matter
what the source and loads are, even if they are out of band. Even a
short or open at DC. In practice, with microwave devices it is very hard
to realise in practice.

--
Dave K

http://www.southminster-branch-line.org.uk/

It is always of the form: [email protected] Hitting reply will work
for a couple of months only. Later set it manually. The month is
always written in 3 letters (e.g. Jan, not January etc)

S

#### Skipp checks in

Jan 1, 1970
0
A chance for a shameless plug to mention the yahoo rfamplifiers
group.

http://groups.yahoo.com/group/rfamplifiers/

cheers,
skipp

: Hi All,

: I'm having a very hard time understanding the full picture on
: amplifier stability, even if I am an engineer. For instance, if we
: select a transistor that is unconditionally stable at our frequency
: band of interest -- let's say from 900MHz to 1000MHz -- but the
: transistor is only conditionally stable at all other frequencies: So,
: we bias, match, and resistively stabilize the transistor so that we
: finally see, in the linear simulator, that K is greater than 1, and B1
: is greater than 0. This should indicate that we now know that the
: amplifier will not oscillate under any input/output impedance
: conditions. But what happens when you place a filter at the input or
: output port of our newly stabilized amplifier? Since the stopbands of
: the filter are anything *but* 50 ohms when the amplifier is looking
: out-of-band, wouldn't there still be a chance that this
: "unconditionally stable" amplifier could oscillate, since it is only
: based on a conditionally stable transistor?

: Thanks!

: -Bill

T

#### Tim Wescott

Jan 1, 1970
0
billcalley said:
Hi All,

I'm having a very hard time understanding the full picture on
amplifier stability, even if I am an engineer. For instance, if we
select a transistor that is unconditionally stable at our frequency
band of interest -- let's say from 900MHz to 1000MHz -- but the
transistor is only conditionally stable at all other frequencies: So,
we bias, match, and resistively stabilize the transistor so that we
finally see, in the linear simulator, that K is greater than 1, and B1
is greater than 0. This should indicate that we now know that the
amplifier will not oscillate under any input/output impedance
conditions. But what happens when you place a filter at the input or
output port of our newly stabilized amplifier? Since the stopbands of
the filter are anything *but* 50 ohms when the amplifier is looking
out-of-band, wouldn't there still be a chance that this
"unconditionally stable" amplifier could oscillate, since it is only
based on a conditionally stable transistor?

Thanks!

-Bill
The definition of "unconditionally stable amplifier" is that it will
stay stable with any passive load attached -- so unless your filter
presents an impedance with some negative resistance you're OK.

You can see this when you plot stability boundaries on a Smith chart --
the chart doesn't really end at the gamma = 1 circle, it continues on
outward for reflection coefficients higher than one, which imply
negative resistances. So if the stability boundary is entirely outside
the usual chart it doesn't mean that _nothing_ will make the amplifier
unstable, it just means that nothing _passive_ will make the amplifier
unstable.

B

#### billcalley

Jan 1, 1970
0
Thanks Tim and Dave! Great stuff!
I'm a bit confused by Dave's answer, since I had strongly thought
that there *was* such a thing as unconditionally stable transistors
(stability as calculated by the Rollett Stability Factor 'K', and the
Stability Measure 'B1'), and not just unstable amplifiers -- and that
in-phase feedback and gain made the amplifiers into oscillators. I'm
probably missing something here though...

-Bill

G

#### Gerhard Hoffmann

Jan 1, 1970
0
Hi All,

I'm having a very hard time understanding the full picture on
amplifier stability, even if I am an engineer. For instance, if we
select a transistor that is unconditionally stable at our frequency
band of interest -- let's say from 900MHz to 1000MHz -- but the
transistor is only conditionally stable at all other frequencies: So,
we bias, match, and resistively stabilize the transistor so that we
finally see, in the linear simulator, that K is greater than 1, and B1
is greater than 0. This should indicate that we now know that the
amplifier will not oscillate under any input/output impedance
conditions.

Yes, if the K & B1 conditions hold for _all_ frequencies, not only those
you are interested in. Then it doesn't even matter if the transistor
initially was unstable on the intended operation frequency.
But what happens when you place a filter at the input or
output port of our newly stabilized amplifier? Since the stopbands of
the filter are anything *but* 50 ohms when the amplifier is looking
out-of-band, wouldn't there still be a chance that this
"unconditionally stable" amplifier could oscillate, since it is only
based on a conditionally stable transistor?

It would not oscillate, no matter what the source or load impedance
were. (Well, unless source or load exhibit negative return loss, but that
would be unfair.)
It would oscillate only if there was _additional_ external feedback
That feedback might be invisible in your circuit diagram, like
waveguide modes of your box or long vias thru thick epoxy..

regards, Gerhard

J

#### Joerg

Jan 1, 1970
0
Hello Bill,
I'm a bit confused by Dave's answer, since I had strongly thought
that there *was* such a thing as unconditionally stable transistors ...

There aren't. This would require ratification of the UST act in congress.

SCNR, Joerg

T

#### Tim Wescott

Jan 1, 1970
0
billcalley said:
Thanks Tim and Dave! Great stuff!
I'm a bit confused by Dave's answer, since I had strongly thought
that there *was* such a thing as unconditionally stable transistors
(stability as calculated by the Rollett Stability Factor 'K', and the
Stability Measure 'B1'), and not just unstable amplifiers -- and that
in-phase feedback and gain made the amplifiers into oscillators. I'm
probably missing something here though...

-Bill
Transistors have enough capacitance from collector to base (or drain to
gate) that with the right inductances on the collector (drain) and base
(gate) they will oscillate. Many overtone crystal oscillators are made
this way, with the crystal providing inductive reactance to the base and
an LC tuned circuit providing inductive reactance to the collector.

There are many, many circuits for which you just don't have to worry
about a transistor bursting into oscillation -- perhaps this is why you
thought they were unconditionally stable?

--

Tim Wescott
Wescott Design Services
http://www.wescottdesign.com

B

#### billcalley

Jan 1, 1970
0
Thanks Gerhard and Tim for the clarifications. Much appreciated!!

-Bill

R

#### [email protected]

Jan 1, 1970
0
The capital K refers to the overall (device embedded in the circuit)
stability, k is the Rollet stability factor. Even if k <1 at some
frequencies one can make K>1 at all frquencies by lossy embedding and
or feedback. Having done this the overall circuit will be
unconditionally stable for all non-feedback terminations with
reflection coefficients no greater than1.
Dick

B

#### billcalley

Jan 1, 1970
0
Thanks Dick! I hadn't known that there was a K and a k. Makes sense
though, and the books never seem to fully clarify this either.

-Bill

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