(Random internet screen grab)

I recently ran
across a “Ultra Low Noise Moving Magnet Phono Preamp” that was
built with four paralleled LT1028 low noise OPAMP’s, and
immediately thought: “That will make the noise worse” simply
because I have built amplifiers like this before and I knew that to
achieve a low total system noise that the source resistance would
have to be extremely low, well below 1 ohm, which a Magnetic Phono
Cartridge is not *.

*Note: We are going to do a 'rough cut' analysis here, looking at the main 1st order effects only. For instance we will ignore for the time being the resistance in the inverting input to the OPAMP(s), they add noise but are low enough to pale in comparison to the Phone Cartridge resistance. We will ignore for the time being that the Phono Cartridge impedance is not the same at DC and 1 kHz. Finally we will not include the effects of the RIAA filter that Phono Preamps always have. For a complete detailed analysis see the section: "Extra Bonus 2" below.*

**Parallel OPAMP’s For Lower Noise**

You have probably
seen this circuit before, it is even shown in the LT1028 Data Sheet
[1]. It works on the principle: If you parallel uncorrelated noise
sources, say: Four LT1028 OPAMPs, the combined RMS voltage noise will
be reduced by the Sqrt(N), where N is the number of devices
paralleled. This has been used successfully with OPAMP and Voltage
References in ultra low noise circuits for decades. Figure 1 shows
the basic configuration.

**Figure 1 – Simplified schematic of the basic proposed “Ultra Low Noise Phono Preamp” using four LT1028 OPAMP’s in a parallel combination to get the lowest possible input voltage noise. But is this really the lowest noise in the actual application circuit?**

What most people
forget is that in the case of an OPAMP, the input current noise
increases by the same Sqrt(N). We will see how this fits together a
bit later on.

**Source Resistance***

In the case of a
moving Magnet Phono Cartridge the source resistance is the cartridge
itself and these, while being variable between manufacturers, do have
some common characteristics [2].

The stylus is
attached to a magnet that moves in the record grooves. This magnet
then moves next to a stationary coil and this interaction of moving
magnetic field produces a voltage in the magnetic coil, this voltage
when amplified then produces the sound that we hear. Figure 2 show a
first order model for a typical Moving Magnet Phono Cartridge and
specified load of 250pF || 47 kOhms for a flat frequency response.

**Figure 2 – Simplified model of a Moving Magnet Phono Cartridge including the connecting Coax Cable and the Specified Load: 250pF || 47 kOhms. 100pF of the load capacitance is usually included in the Preamp.**

These coils are
wound with many turns of very fine magnet wire as the inductance
needs to be large to make enough voltage when playing a record to be
useable. This long length of fine magnet wire has a resistance which
is quite large, in fact it can be upwards of 1500 Ohms as Table 1
shows.

**Table 1 – Two representative Shure Moving Magnet Phono Cartridge types are presented. These seem to be representative of the typical spread in values of all commercial Phono Cartridges.**

As can be seen there
is a quite large DC resistance in this type of design. If we use the
lower number of 630 Ohms from Table 1 for the rest of our examples,
we can see that this resistance has a noise voltage all its own which
can be found by the familiar resistor thermal noise equation of,

Vnoise_rms = Sqrt(4
* Kb * T * R) Resistor noise in a 1 Hz Bandwidth [3].

At room temperature
this equation simplifies to,

nVnoise_rms = 0.13
* Sqrt(R) Resistor noise at 27 Deg C (equation 1)

The units here are:
“Nanovolts per Root Hertz”, where the Nanovolts are: “RMS”
(Root Mean Squared). We will write these units as this for the
remainder of this article: nV/rt-Hz

The “Root Hertz”
Simply reminds us that the values are normalized to a 1 Hz bandwidth,
that makes the subsequent math easy. If we want to know the total
integrated noise in say a 20 kHz bandwidth, then we would just
multiply the value by Sqrt(20,000) or 141, then we would get a
cancellation of the rt-Hz term and just be left with the Nanovolts
RMS value.

Applying Equation 1,
to the Phono Cartridge DC resistances and you can see that the source
itself, at low frequencies produces a thermal noise voltage of,

0.13 * Sqrt(630) =
3.2 nV/rt-Hz

0.13 * Sqrt(1550) =
5.1 nV/rt-Hz

We clearly just
found out that just the cartridge itself has a thermal noise of 3.2
to 5.1 nV/rt-Hz for these two, but representative cartridges.

Looking at the data
sheet we can also see that the LT1028 has a typical noise voltage of
just 0.85 nV/rt-Hz at midband or 1 kHz.

**Disconnect 1 -**

Armed with only the
knowledge of the equivalent circuit of the Phono Cartridge and with
only one multiplication (equation 1), we can see that the circuit
noise floor is going to be set by the DC resistance of the Phono
Cartridge and not the LT1028 amplifier.

This is why the
“First Audio OPAMP”, the NE5534A produced by Phillips / Signetics
in the mid 1970’s was so popular, it was designed to have an input
noise equivalent to what the application circuit demanded, yes the
NE5534 had an input voltage noise of typically 3.5 nV/rt-Hz. Look at
that, it was designed that way for a purpose, as it matches the
typical noise of a Magnetic Phono Cartridge.

The first disconnect
is: Going to ‘Heroic’ lengths to lower the input amplifiers noise
in this case is not going to improve the entire systems noise
performance because the noise floor is set by the sensor itself and a
single LT1028 is already 3 times lower than probably the best Phono
Cartridge.

**Disconnect 2 -**

One might ask: “Well
what does it matter if we parallel 4 preamps? It doesn’t make the
noise worse does it?”, let’s see...

Remember when we
discussed what paralleling OAPMP’s really does? It reduces the
voltage noise by Sqrt(N) BUT it increases the current noise by the
same Sqrt(N). In a normal OPAMP circuit, at low source resistances
the voltage noise will dominate and at high source resistances the
current noise will dominate. In between these extremes there is an
interaction with the source resistance itself.

An easy calculation
to make is to divide the voltage noise by the current noise at a
given frequency to come up with an equivalent noise resistance for
the OPAMP, this is sometimes called Ropt and it will be the point
where a source resistance of the same value will be equal to the
total voltage and current noise of the OPAMP, producing a combined
value that is 3 dB higher (or 1.41 times) than each separately.

For the LT1028 the
data sheet the noise values at 1 kHz are,

Vn = 0.85 nV/rt-Hz

In = 1.0 pA/rt-Hz

Hence Ropt at 1 kHz
is found to be,

Ropt = 0.85e-9 /
1.0e-12 = 850 Ohms

We can say that for
the LT1028 at 1 kHz

A source
resistance of << 850 Ohms and you will be limited by the

**voltage**noise of the OPAMP
A source
resistance of >> 850 Ohms and you will be limited by the

**current**noise of the OPAMP
If we parallel 4 x
LT1028’s we get the following Ropt,

Ropt_4x = (0.85e-9
/ Sqrt(4)) / (1.0e-12 * Sqrt(4)) = 213 Ohms

Ropt has been
lowered by N times the value of a single amplifier, in this example N
is equal to 4, and the new Ropt is: 850/4 = 213 Ohms.

In this particular
case of four paralleled LT1028’s you can see that the current noise
will always be dominate since the lowest Phono Cartridge resistance
that I found was 630 Ohms.

Ropt is a quick and
useful calculation to see where your OPAMP selection stands in
relation to the source resistance.

The disconnect #2
is: “Just using more amplifiers will not lead to an improvement in
total system voltage noise if Ropt is above the sensor resistance.”

**A Closer Look**

A closer examination
of the system and all its various noise sources shows why,

Note: When adding voltage noise terms together, we use the Root Sum Square method (RSS) or,

Note: When adding voltage noise terms together, we use the Root Sum Square method (RSS) or,

Result = Sqrt(Val1*Val1 + Val2*Val2)

**Table 2 – The voltage noises add in RSS fashion, the current noise is multiplied by the source resistance to get the equivalent voltage noise effect of the two. In the 1x preamp case: 1pA/rt-Hz * 630 = 0.63 nV/rt-Hz. The situation is even worst if we use the 1500 Ohm Phono Cartridge in the bottom example and the 4x configuration. Then the total system noise would be a whopping: 8.2 nV/rt-Hz.**

As can be seen in
Table 2, while the voltage noise of 4 X LT1028’s does indeed drop
the voltage noise of the Preamp by 50%, but
the additional current noise increases the of noise developed across
the sensors resistance by 4 times and finally the total system noise
is actually 23% higher with 4 paralleled amplifiers and this is for
the low source resistance Phono Cartridge, the result gets even worse
for the 1.5k Ohm version of the Phono Cartridge.

We could have
predicted this by taking a quick look at Ropt at the design stage.
Since the Ropt of a single LT1028 is some 850 Ohms, and this is smack
in the middle of the range of our expected Phono Cartridges, we know
that paralleling more of these amplifiers will not help in reducing
the total voltage noise in the circuit as the current noise will take
over and really a single LT1028 is going to be pretty optimum as it
is.

**Figure 3 – Total system input integrated noise, referred to the input, over a 10 Hz to 20 kHz bandwith as simulated for a 1x and 4x LT1028 Preamp when measuring the 630 Ohm Phono Cartridge and specified load of Figure 1. As can be seen the 1 x LT1028 produces lower total integrated system noise (upper plot). Adding four paralleled LT1028’s in this example made the total integrated system noise worse (lower plot). This simulation includes the frequency effects of the Phono Cartridge source resistance.**

Total integrated noise at 20 kHz – 1 x OPAMP’s - Upper Trace =
3.6 uV RMS

Total integrated noise at 20 kHz – 4 x OPAMP’s - Lower Trace =
4.2 uV RMS

Bottom Line – Four
Amplifiers actually has 17% worst total system noise in a 20 kHz
bandwidth, even for the lowest resistance Phono Cartridge. The
situation is even worse if the 1550 Ohm cartridge is considered.

*Side Note #1: These bipolar based low noise OPAMP’s, almost always have a higher 1/f frequency for the current noise than the voltage noise 1/f frequency. For the LT1028 the 1/f corner on the voltage noise is approximately 3.5 Hz, well below the start of the audio band. While the 1/f Corner for the current noise is around 850 Hz. This will mean that the low frequency noise will be increasing in the audio band if the OPAMP is operating where the current noise times source resistance is the dominant noise source of the circuit.*

*Side Note #2: On Bipolar OPAMP’s with input bias current compensation, a large portion of the bias current noise can be due to the compensation current, this compensation current is always generated by one transistor inside the OPAMP and then split to the two OPAMP inputs. Some of the input current noise is therefore correlated between the two inputs [4]. This means that at higher source resistances, the total system noise may be less with circuits that use balanced source resistances. The amount of correlation is never listed explicitly on the data sheet and only Linear Technology regularly puts this information in their performance curves on their data sheets. For all other OPAMP’s in the world, you will just have to measure this for yourself. For the LT1028 the amount of current noise correlation has proven to be around 25%.*

**Conclusion -**

Don’t forget that
total system noise depends on not only the Voltage Noise Source
Resistance, the OPAMP itself, and also the contribution of the
OPAMP’s Current Noise times the Source Resistance.

Make sure that you
know what the Source Resistance of the thing you are measuring before
picking and trying to optimize the OPAMP Preamp.

Use the very simple
to calculate value: “Ropt” to see where your perspective OPAMP
fits in relation to the system source resistance. For most typical
circuits where you are trying to minimize total voltage noise, you
want the Ropt to be 2 to 10 times higher than the system source
resistance. If possible.

For this example
Phono Preamp with it’s 630 to 1500 Ohm source resistance, a single
LT1028 is not the best choice with a Ropt of 850 Ohms, and you will
pay a premium price for it’s ultra low noise performance. The more
reasonably priced NE5534A is also a perfectly reasonable and lower
cost choice with it’s Ropt of 8700 Ohms @ 1 kHz.

If you pick an OPAMP
who’s total voltage and current noise contribution (Ropt) is
exactly equal to the source resistance, the combined voltage noise
will be 3 dB higher (1.414 higher or 40% in linear terms) than the
source resistance alone.

**Bonus Curve -**

I presented a singe
value for Ropt, the one we read off the data sheet from the given
values at 1 kHz. However, Ropt is not a single value, it varies with
frequency just as the Voltage Noise and Current Noise do.

A complete Ropt
curve versus frequency for the LT1028 is shown in Figure A. This
curve is derived from the typical voltage noise and current noise
figures from the LT1028 data sheet. A curve like this is useful to
have for all your low noise OPAMP’s as it is a handy reminder of
how Ropt changes with frequency for a particular OPAMP, because many
circuits do not operate at single frequencies, some may operate at
extremely low frequencies or at high frequencies exclusively. With a
Ropt plot versus Frequency you can make even better informed choices
on your amplifiers interaction with your source resistance.

**Figure A – Ropt is not a single number, but actually varies with frequency as the Voltage and Current Noise of the OPAMP vary. Her we can see that the midband value of 825 Ohms drops as low as 200 Ohms at 10 Hz to a high of 925 Ohms at 20 kHz. It is good to keep this in mind when designing for circuits with either very low or very high bandwidth centers, because not every circuit operates at 1 kHz which is where the typical voltage an current noise vlaues are given. I make these curves with the help of a template that I have made for the LibreOffice Spreadsheet program [5].**

**Footnote:**

* The term I use
here as ‘Source Resistance’ means the real part of the source
impedance, and it is a number that usually varies with frequency.

**Extra Bonus 2 -**

Art Kay of Texas Instruments wrote an really excellent book on all things OPAMP noise, it even details how to simulate the noise with Spice. Art has kindly posted a zip file with all the articles at the link below,

https://e2e.ti.com/support/amplifiers/f/14/t/435427?App-Notes-for-Op-Amp-Noise-by-Art-Kay

**References:**

[1] LT1028 Data
Sheet www.analog.com

[2] Reference Shure
Phono Cartridge Data Sheets:

M97xE User Guide,
2008

M91G Data Sheet,
1970

[4] Solomon, James -
“The

*monolithic op amp*: A tutorial study” IEEE Journal of Solid-State Circuits, vol. 9, pp. 314 – 332, December 1974(Also available as an application note at ti.com)
[5] Open Source
Office Software – www.LibreOffice.org

**Article By: Steve Hageman / www.AnalogHome.com**

*We design custom: Analog, RF and Embedded systems for a wide variety of industrial and commercial clients. Please feel free to contact us if we can help on your next project.*

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