# Common collector Colpitts oscillator frequency formula

Started by November 2, 2018
```Could some electronics guru please help ? I am trying to
find the frequency of oscillation for a common collector
Colpitts oscillator ?

For a common emitter Colpitts oscillator, the frequency
of oscillation is focs = 1/(2*PI*sqrt(L*Ct)) where Ct
is the equivalent capacitance of the two series
capacitors. The resonator is used as PI circuit,
with a series inductor and 2 shunt capacitors
at the two wnds of the inductor.

On the other hand, the resonator used fir the
common collector Colpitts oscillator, there
are two output nodes, first at the end of the
inductor, and the other at the end of the first
capacitor of the series capacitor pair. Wjat
would the oscillation frequency be in this case ?

Any hints/suggestions/pointers to relevant
information would be very helpful. Thanks in

```
```On 2.11.18 12:40, dakupoto@gmail.com wrote:
> find the frequency of oscillation for a common collector
> Colpitts oscillator ?
>
> For a common emitter Colpitts oscillator, the frequency
> of oscillation is focs = 1/(2*PI*sqrt(L*Ct)) where Ct
> is the equivalent capacitance of the two series
> capacitors. The resonator is used as PI circuit,
> with a series inductor and 2 shunt capacitors
> at the two wnds of the inductor.
>
> On the other hand, the resonator used fir the
> common collector Colpitts oscillator, there
> are two output nodes, first at the end of the
> inductor, and the other at the end of the first
> capacitor of the series capacitor pair. Wjat
> would the oscillation frequency be in this case ?
>
> Any hints/suggestions/pointers to relevant
> information would be very helpful. Thanks in

For starters, have a look at
<http://fourier.eng.hmc.edu/e84/lectures/ch4/node12.html>.

--

-TV

```
```dakupoto@gmail.com wrote:
> find the frequency of oscillation for a common collector
> Colpitts oscillator ?
>
> For a common emitter Colpitts oscillator, the frequency
> of oscillation is focs = 1/(2*PI*sqrt(L*Ct)) where Ct
> is the equivalent capacitance of the two series
> capacitors. The resonator is used as PI circuit,
> with a series inductor and 2 shunt capacitors
> at the two wnds of the inductor.
>
> On the other hand, the resonator used fir the
> common collector Colpitts oscillator, there
> are two output nodes, first at the end of the
> inductor, and the other at the end of the first
> capacitor of the series capacitor pair. Wjat
> would the oscillation frequency be in this case ?

Schematics would help us understand what the problem
is.

Apart from the effects of parasitic capacitances, which
I did not attempt to analyze, the same. The tank is
still a single L in parallel with a series pair of C's,
even if that may not be immediately obvious from the
schematic diagram.

Removing all secondary considerations, I think of a
Colpitts as basically this:

+---L---+----+
|       |    |
|     |/     |
+-----|      C
|     |\ e   |
|       |    |
+---C---+----+

You then choose a ground point and re-arrange and
add components to get the biasing right without
upsetting the AC equivalent circuit.

If you exchange L's for C's and the reverse, it would
be a Hartley oscillator. If you replace the L by a
series L-C, it would be a Clapp. If you replace the
L by a quartz crystal, it would be a Pierce. There
are more.

Jeroen Belleman
```
```dakupoto@gmail.com wrote:
> find the frequency of oscillation for a common collector
> Colpitts oscillator ?

Not a gure, but looked at exactly this problem.  In first
approximation regardless of oscilator type  (Colpitts, Hartey,
common emiter, common base, common collector) you have
frequency of resonant tank.  If you need more accurate
results you need to look at parasitics and imperfections
of elements.  Most of the time it is enough to pretend
rest of circult is perfect, but L and C have different
value.  For accurate results you would need real guru.
But beware: apparently nobody can accurately compute
amplitude of oscilation and it would be extremally
weird if freqency were completely independent from
amplitude.  To be clear: dependence on amplitude is
certainly smaller than other effects like change of
transistor parameters with temperature, so for most
practical purposes is negligible.  But again, for
most practical purposes frequency of resonant tank
is good enough.

To state the obvous: in resonat tank the two capacitors
form series connection, so you use formula for resulting
capacitance.  Also, in common collector Colpitts
connecting emiter between capacitors give you effect
of transformer: higher voltage on base.  Common collector
has voltage gain less than 1, so this "transformer
effect" is essential to get oscilations.

--
Waldek Hebisch
```
```antispam@math.uni.wroc.pl wrote:

> dakupoto@gmail.com wrote:
>> find the frequency of oscillation for a common collector
>> Colpitts oscillator ?

> But beware: apparently nobody can accurately compute
> amplitude of oscilation and it would be extremally
> weird if freqency were completely independent from
> amplitude.

You set the amplitude by increasing the current to the oscillator. For a
common collector Colpitts, the amplitude will change very little from one
device to another. The common collector Colpitts also has the advantage
that the feedback capacitors tend to swamp out any changes in device
parameters.

There are a number of techniques to reduce the 1/f noise. These will also
tend to stabilize the amplitude.

Changing the transistor type can have a large effect on the amplitude,
especially if you are running at high frequencies.

For a Pierce oscillator, you change the signal into the tank by changing
the feedback resistor.

For examples, see

Oscillator.zip

```
```<antispam@math.uni.wroc.pl> wrote in message
news:priile\$jvi\$1@z-news.wcss.wroc.pl...
> Not a gure, but ...

"It is dark. You are likely to be eaten by a gure."

:^)

Tim

--
Seven Transistor Labs, LLC
Electrical Engineering Consultation and Design
Website: https://www.seventransistorlabs.com/

```
```On Friday, November 2, 2018 at 6:21:37 PM UTC-4, anti...@math.uni.wroc.pl wrote:
> dakupoto@gmail.com wrote:
> > find the frequency of oscillation for a common collector
> > Colpitts oscillator ?
>
> Not a gure, but looked at exactly this problem.  In first
> approximation regardless of oscilator type  (Colpitts, Hartey,
> common emiter, common base, common collector) you have
> frequency of resonant tank.  If you need more accurate
> results you need to look at parasitics and imperfections
> of elements.  Most of the time it is enough to pretend
> rest of circult is perfect, but L and C have different
> value.  For accurate results you would need real guru.
> But beware: apparently nobody can accurately compute
> amplitude of oscilation and it would be extremally
> weird if freqency were completely independent from
> amplitude.  To be clear: dependence on amplitude is
> certainly smaller than other effects like change of
> transistor parameters with temperature, so for most
> practical purposes is negligible.  But again, for
> most practical purposes frequency of resonant tank
> is good enough.
>
> To state the obvous: in resonat tank the two capacitors
> form series connection, so you use formula for resulting
> capacitance.  Also, in common collector Colpitts
> connecting emiter between capacitors give you effect
> of transformer: higher voltage on base.  Common collector
> has voltage gain less than 1, so this "transformer
> effect" is essential to get oscilations.
>
> --
>                               Waldek Hebisch

Yes, I fully agree with you say. My problem is that I am
examining an old common collector Colpitts oscillator design with a target oscillation frequency of 75 MHz.
The engineer who designed it has moved to a different company some tears ago. The value of each of the two
capacitors in the series pair is 39pF, and the inductor is  0.2uH. So the equivalent capacitance is 19.5pF, and
usig expression:
fosc = 1/(2.0*PI*sqrt(L*Ceqv)) the numerical value of
the oscillation frequency is:
fosc = (10^9)/(2*PI*sqrt(3.9)) = 80.0MHz.
The SPICE netlist, when simulated gives oscillation
frequency of 77 MHz. So far, so good.
The design is a bit unusual as the inductor is connected
directly to the BJT base biasing voltage divider, with a
1nF capacitor at the same node to ground, to suck out
AC.
The problem is that if I try to use a different fosc, e.g., 150 MHz, and compute a different set of component
values(for this new oscillation frequency) the oscillator
latches up.
To design the common mode amplifier, I use the standard
design rules Ve is approx. 0.5Vcc, Vb = Ve + 0.65 and
maximum biasing current is 10x(Ic/beta(min)), where it
is assumed that Ic is approx. equal to Ie, which in turn
is set by the designer. I am using 2N5179, for which
beta(min) = 25, and Ic(max) = 50mA. The amplifier stage
simulates perfectly fine.

So, what could be causing the latchup ? Any hints/suggestions ?

```
```On Friday, November 2, 2018 at 9:06:59 PM UTC-4, Tim Williams wrote:
> <antispam@math.uni.wroc.pl> wrote in message
> news:priile\$jvi\$1@z-news.wcss.wroc.pl...
> > Not a gure, but ...
>
> "It is dark. You are likely to be eaten by a gure."
>
> :^)
>
> Tim
>
> --
> Seven Transistor Labs, LLC
> Electrical Engineering Consultation and Design
> Website: https://www.seventransistorlabs.com/

Watch out yourself. Halloween is approaching --
nights are colder and darker and 'gures' have the irritating habit of popping up at the most unexpected
places.

```
```On 03/11/18 12:05, dakupoto@gmail.com wrote:

>
> Yes, I fully agree with you say. My problem is that I am
> examining an old common collector Colpitts oscillator design with a target oscillation frequency of 75 MHz.
> The engineer who designed it has moved to a different company some tears ago.

Sounds like you miss him...

> The value of each of the two
> capacitors in the series pair is 39pF, and the inductor is  0.2uH. So the equivalent capacitance is 19.5pF, and
> usig expression:
> fosc = 1/(2.0*PI*sqrt(L*Ceqv)) the numerical value of
> the oscillation frequency is:
> fosc = (10^9)/(2*PI*sqrt(3.9)) = 80.0MHz.
> The SPICE netlist, when simulated gives oscillation
> frequency of 77 MHz. So far, so good.
> The design is a bit unusual as the inductor is connected
> directly to the BJT base biasing voltage divider, with a
> 1nF capacitor at the same node to ground, to suck out
> AC.
> The problem is that if I try to use a different fosc, e.g., 150 MHz, and compute a different set of component
> values(for this new oscillation frequency) the oscillator
> latches up.
> To design the common mode amplifier, I use the standard
> design rules Ve is approx. 0.5Vcc, Vb = Ve + 0.65 and
> maximum biasing current is 10x(Ic/beta(min)), where it
> is assumed that Ic is approx. equal to Ie, which in turn
> is set by the designer. I am using 2N5179, for which
> beta(min) = 25, and Ic(max) = 50mA. The amplifier stage
> simulates perfectly fine.
>
> So, what could be causing the latchup ? Any hints/suggestions ?

I have trouble seeing how such a simple circuit can latch up.
What are the node voltages when that happens?

Did you bypass the collector to GND?

Jeroen Belleman

```
```On 3.11.18 13:05, dakupoto@gmail.com wrote:
> On Friday, November 2, 2018 at 6:21:37 PM UTC-4, anti...@math.uni.wroc.pl wrote:
>> dakupoto@gmail.com wrote:
>>> find the frequency of oscillation for a common collector
>>> Colpitts oscillator ?
>>
>> Not a gure, but looked at exactly this problem.  In first
>> approximation regardless of oscilator type  (Colpitts, Hartey,
>> common emiter, common base, common collector) you have
>> frequency of resonant tank.  If you need more accurate
>> results you need to look at parasitics and imperfections
>> of elements.  Most of the time it is enough to pretend
>> rest of circult is perfect, but L and C have different
>> value.  For accurate results you would need real guru.
>> But beware: apparently nobody can accurately compute
>> amplitude of oscilation and it would be extremally
>> weird if freqency were completely independent from
>> amplitude.  To be clear: dependence on amplitude is
>> certainly smaller than other effects like change of
>> transistor parameters with temperature, so for most
>> practical purposes is negligible.  But again, for
>> most practical purposes frequency of resonant tank
>> is good enough.
>>
>> To state the obvous: in resonat tank the two capacitors
>> form series connection, so you use formula for resulting
>> capacitance.  Also, in common collector Colpitts
>> connecting emiter between capacitors give you effect
>> of transformer: higher voltage on base.  Common collector
>> has voltage gain less than 1, so this "transformer
>> effect" is essential to get oscilations.
>>
>> --
>>                                Waldek Hebisch
>
> Yes, I fully agree with you say. My problem is that I am
> examining an old common collector Colpitts oscillator design with a target oscillation frequency of 75 MHz.
> The engineer who designed it has moved to a different company some tears ago. The value of each of the two
> capacitors in the series pair is 39pF, and the inductor is  0.2uH. So the equivalent capacitance is 19.5pF, and
> usig expression:
> fosc = 1/(2.0*PI*sqrt(L*Ceqv)) the numerical value of
> the oscillation frequency is:
> fosc = (10^9)/(2*PI*sqrt(3.9)) = 80.0MHz.
> The SPICE netlist, when simulated gives oscillation
> frequency of 77 MHz. So far, so good.
> The design is a bit unusual as the inductor is connected
> directly to the BJT base biasing voltage divider, with a
> 1nF capacitor at the same node to ground, to suck out
> AC.
> The problem is that if I try to use a different fosc, e.g., 150 MHz, and compute a different set of component
> values(for this new oscillation frequency) the oscillator
> latches up.
> To design the common mode amplifier, I use the standard
> design rules Ve is approx. 0.5Vcc, Vb = Ve + 0.65 and
> maximum biasing current is 10x(Ic/beta(min)), where it
> is assumed that Ic is approx. equal to Ie, which in turn
> is set by the designer. I am using 2N5179, for which
> beta(min) = 25, and Ic(max) = 50mA. The amplifier stage
> simulates perfectly fine.
>
> So, what could be causing the latchup ? Any hints/suggestions ?

If this is a simulation, you often need to set up some
unbalanced initial condition to make the oscillation
start up.

In real circuit, there is enough noise which helps the
start-up.

--

-TV

```