# The Transcoductance Capacity Format

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

|     490nA ______|    |           |___/\  /\  /\_

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/