**This invention concerns itself with what happens when
a
large number of transconductance amplifiers get put into
the same integrated circuit. Having a pre-distortion or linearizing **

**circuit at the input to a transconductance amplifier is**

**actually performing a critical function in addition to**

**lowering distortion. They are also performing a
temperature**

**scaling function. **

**The linearizing diodes used in the LM13700 were suited**

**to a +/-15V supply world. Signal levels were often set **

**to several volts. At such levels, resistors could be **

**used without introducing much noise, or distortion, or
offset.**

**What may not be obvious is that the linearizing diodes**

**are also gain scaling the input signal of a
transconductance**

**amplifier to track absolute temperature. This is
important**

**because the current to voltage relationship of
transconductance **

**amplifiers happen to decrease relative to absolute
temperature. **

**A simple plot of the transfer function of a two
transistor**

**input stage can show that relationship.**

**Temperature gain balancing is happening when any type**

**of linearizing or pre-distortion circuitry is applied
to**

**the input of a transconductance amplifier. But what
happens**

**when a transconductance amplifier input stage is using **

**distortion cancellation, and does not use a
pre-distortion **

**circuit?**

**The transfer circuit for the circuit above still has
its**

**gain dropping relative to absolute temperature. But the**

**distortion curves shown below shows that the
distortion versus**

**input signal is also highly temperature dependent.**

**Normally the input level gets picked as a trade off
between**

**distortion and signal to noise. Without any
pre-distortion**

**circuitry, there is now a temperature relationship
associated with**

**distortion.**

** **

**If signal is instead treated in terms of being a
percentage of**

**the maximum output current, then both temperature**

**and bias current are removed from the transconductance **

**amplifier's distortion curve. Think of the maximum
output**

**current as being its channel capacity. **

**A 50% rule can be used to relate an output current**

**capacity to an effective input voltage capacity.**

**Transconductance amplifiers are usually pretty**

**linear up to the point where their putting out**

**around than 50% of their maximum output current. **

**Define the input voltage to be at its 50% maximum**

**input level when its output current is at 50% of**

**its maximum output level. So maximum input capacity**

**voltage for that input stage can be treated as twice **

**that 50% level. **

**Using transconductance amplifiers to build things like**

**voltage controlled filters can show that thinking of**

**signal in terms of either voltage levels or current
levels**

**is going to get confusion, especially when trying to
maintain**

**an optimum distortion levels versus signal to noise
ratios over a**

**-55C to 125C temperature range. Thinking in terms of **

**percentages of channel capacity can make things much
easier.**

**Think of a transconductance amplifier operating at 50%**

**capacity as putting out current at 50% of its maximum**

**output current, and having an input voltage being **

**applied which is at 50% of the recommended input level. **

**Now regardless of the bias current for the
transconductance **

**amplifier, it will still be operating at 50% capacity.
If the **

**input voltage gain is set to track absolute
temperature,**

**then operating at 50% channel capacity will be
independent**

**of both the transconductance amplifier's bias current **

**and temperature. **

**In in the schematic above, assume all resistors have
zero**

**temperature coefficients. How the bias current for the **

**transconductance amplifiers get generated is key. **

**Suppose the 1uA current is derive from a collector
current of**

**an NPN transistor which has its base connected to a
bandgap**

**and has a 600K resistor from its emitter to ground.
This will **

**force a temperature tracking 600mV across a 600K
resistor. By using **

**a 90KOhm resistor at the output of the first
transconductance **

**amplifier, it automatically supplies an output signal**

**to the second transconductance amplifier with a signal
**

**in the same 50% channel capacity format. And this can
be apply**

**onward to a further series of transconductance stages.**

**Things however may look a little strange when looking
at**

**the transfer curves of the transconductance amplifiers.**

**Over temperature, they will all have the same slope.**

**In other words, the current to voltage relationship**

**resembles a resistor which has a zero temperature
coefficient.**

**But output current capacity and for that matter the**

**input voltage capacity will all increase as absolute**

**temperature increases. So if the input signal also**

**tracks the channel capacity, then the signal will
operate**

**at a fixed percentage of channel capacity regardless of**

**temperature. In this special case, the current to
voltage **

**relationship (impedance) is temperature independent.
The **

**signal levels in terms of percentages of either
currents or **

**voltages are also temperature independent.**

**Now assume all resistors will increase exactly 33.3%
for**

**a 100C increase in temperature. Now when the 600mV is
applied**

**across the 600K resistor, the 1uA current will remain
constant**

**over temperature. But the current to voltage
relationship **

**for the transconductance amplifier will look like a
resistor**

**which is increasing by 33.3% for a 100C increase. So
this will**

**introduce a 33.3% reduction in output current. But in
this**

**case, the 90K resistor will also be increasing 33.3%.
So**

**the output voltage gain will still be able to drive
the following**

**transconductance amplifier at 50% capacity. So both**

**transconductance amplifiers will still be operating at
50%. **

**Two details should be noted. The TC of the resistor
used to**

**generate the bias current for a transconductance
amplifier**

**will define the TC of the transconductance amplifier.
If the**

**TC of the transconductance amplifier matches the TC of
the**

**load impedance at its output, then signal in terms of a **

**percentage of channel capacity can be maintained from
stage**

**to stage. **

**So the TC of the resistor which has 600mV forced
across it**

**only needs to match the TC of the load impedance. This**

**is also possible for voltage controlled filters. The
TC of**

**capacitors is near zero. Using a Sichrome resistor
would**

**come close to matching the zero TC. **

**Transconductance amplifiers appear to want to work in a **

**dimension less or pure ratio mode. For instance the
bias current**

**applied to a transconductance amplifiers, makes is act
like a**

**resistor, which is set to a ratio of the impedance
loading its output,**

**and defines a temperature independent input to output
gain. Changing**

**the bias current is only changing the ratio. For
filters,**

**the load impedance is a capacitor. This means gain
versus**

**frequency is temperature independent. **

________________________________________

| VCC | | VCC | _|_

| | | | /VCC\

-> <- -> <- \___/

QP1`|___|'QP2 QP4`|___|'QP5 _|_

_ '| | |`_ _ '| | |`_ ///

| |____|VTA2 | |____|VTA5

| | | |

| <- | <-

|_______|' QP3 _____|_______|' QP6

|VTA1 |`_ | VTA4 |`_

| | | | OUT

| **510nA** |_____/|\___
| **490nA** **20nA**

| | | | R1 1 Ohm

| **490n**A
______| | |___/\ /\ /\_

**Vin
= +1mV** _|
|_
| VTA6 _| \/ \/ |

__|'QN1 QN2 `|__ |________|'QN5 _|_

_|_ |`->
<-'| _|_ | |`->
**510nA**
///

/VIN\ | | /// | |

\___/ |__________|VE | ______| VTA7

| _|_ _____ |_ | _|

_|_
/ _ \
_|_ _|_ QN3`|__|__|'QN4 **20nA/1uA = 2%**

/// \/ \/ /VEE\ /// <-'| |`->

/\_/\ \___/ | |
**1mV/51mV = 2%**

\___/ _|_ _|_ _|_

IBIAS _|_ \ / \ / \ /

1uA \ / V VEE V VEE V

V

**The DC offset remains at a fixed ratio of the channel
capacitance.**

**For instance, a 1mV input offset represents a 4%
mismatch for a**

**two transistor input stage. This will in fact produce
a 2% DC offset **

**at the output current port which is independent of
bias current or **

**temperature. Using the 50% rule, this type of input
has a capacity**

**of 51mV. So the DC offset is a 2% error relative to
both the voltage**

**input or current output. A 1mV input offset will
increase with absolute**

**temperature. This is where input offset temperature
drift comes from.**

**So if signal is handled as a percentage of both the
voltage input**

**or current output channel capacity, then in theory
there is no DC **

**temperature drift.
**

** ShotNoise_I_rms
= sqrt(2*q*I_dc*BW)**

** Signal/Noise
= I_dc/sqrt(2*q*I_dc*BW) **

**
= 1/sqrt(2*q*BW/I_dc) **

**
=
1/sqrt(2*q*BW/q*Num_electrons_per_sec) **

**
=
1/sqrt(2*BW/Num_electrons_per_sec)**

**The noise in a transistor differential stage is mainly
all shot noise. **

**The signal to noise ratio is really defined by the
bias current or number **

**of electrons per second that bias up the
transconductance amplifier. **

**Signal to noise ratio can really only be related
relative to the **

**maximum output current. And the signal to noise ratio
will double **

**for a 4X increase in number of electrons per second. **

** **

**
**

**There are different types of input stages. The stage
above has an input **

**voltage capacity of 196mV. All transconductance input
stages have a**

**distortion profile that can be made independent of
temperature, provided**

**the input signal is applied in terms of being a
percentage of the available**

**capacity. So everything can be temperature independent
in the percentage**

**format. That includes signal, dc offset, gain,
frequency response,**

**distortion, and "almost" signal to noise ratio.
Unfortunately resistors **

**inside ICs increase closer to 20% rather than 33.3%
over 100 degrees C. **

**This invention concerns itself with what happens when a**

**large number of transconductance amplifiers get put
into**

**one integrated circuit. One could solve both **

**distortion and temperature scaling issues by putting**

**pre-distortion circuitry in front of every
transconductance**

**amplifier. Or one could handle signal in terms of
percentages **

**of channel capacity, and use distortion cancellation
inputs. **

**The schematic shown above has the Input Converter using**

**a feedback loop to pre-distort and scale the voltage.
Using **

**negative feedback has its advantages. There are ways
to do the **

**job open loop. One pre-distortion stage may always be
needed to **

**convert voltage magnitude to a percentage of channel
capacity. **

**But after the signal is in percentage format, no more
pre-distortion**

**stages are needed. The conversion from percentage
format back to **

**voltage magnitude can easily be done by simply biasing
up the last**

**transconductance amplifier with a more temperature
independent**

**current. **

3.11.10_2.37PM

dsauersanjose@aol.com

Don Sauer

http://www.idea2ic.com/