Monday, June 1, 2020

Is a ‘Heroic’ Low Voltage Noise Amplifier Always Desirable?

(Random internet screen grab)

I recently ran across an “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 the moving magnetic field produces a voltage in the magnetic coil, this voltage when amplified then produces the sound that we hear. Figure 2 shows a first order model for a typical Moving Magnet Phono Cartridge and the specified load of 250pF || 47 kOhms which produces 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 like 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, which 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 datasheet we can also see that the LT1028 has a typical noise voltage of just 0.85 nV/rt-Hz at mid band 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 1970s 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.

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,
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 17% 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 and current noise values 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 a really excellent book and Magazine Article series on all things relating to: "OPAMP noise". The book 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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