Ancient ultra low noise narrow band preamplifier

[mikebg]

Page 3 - Quiz

Quiz:
Here are three circuit diagrams of RFA with operational amplifier.

Indicate which is the worst circuit configuration for metal detecting.

HINTS:
1. Bad circuit configuration is one that amplifies the EMI signal, ie the circuit amplifies the mains frequency and its harmonics.
2. Bad circuit configuration is one that amplifies unnecessary excessive bandwidth of frequencies. For metal detecting is sufficient bandwdth BW <16Hz.
3. Bad circuit configuration is one that generates a lot of additional thermal noise because contains resistors connected in series to RX coil.
4. Bad circuit configuration is that in which the operating point is less stabile because amplifies DC.
5. Bad circuit configuration is one that amplifies frequencies below 100Hz. In this region there are 1/f (flicker) noise.

[mikebg]

Preamp with only one transistor or with opamp IC?

The formula for spectral density of noise voltage generated by a resistance is u°=rt(4kTR) or expressed as square of voltage u°^2=4kTR.
For room temperature T=300K the formula becomes u°^2=1.6E-20*R.
Since resistance of RX coil generates noise, we can make a table like this:

Coil resistance - Spectral density of noise voltage
10 ohm - 0.405 nV/rtHz
20 ohm - 0.566 nV/rtHz
50 ohm - 0.905 nV/rtHz
100 ohm - 1.28 nV/rtHz
200 ohm - 1.79 nV/rtHz
500 ohm - 2.83 nV/rtHz
1000 ohm - 4.05 nV/rtHz
2000 ohm - 5.66 nV/rtHz

Note that when we increase coil resistance twice, the noise not increases twice, but only sqrt2=1.41 times. The notation u° means RMS value. When we calculate peak-to-peak density of noise voltage u p-p, we should multiply the RMS value by 6 to 8 as was shown visual in other postings.
If we compare with above table the noise density of NE5534 given in data sheet u°=4 nV/rtHz, we will see that this IC adds to input so much noise as a 1000 ohm coil or resistor. However our coil has much lower resistance, for example 50 ohm. Remember that a low noise transistor generates noise with its rbb'<50 ohm.
When we use IC operational amplifier, we should connect to its inverting input a noise generating resistor noted as R1 in the attached circuit diagram. How to calculate resistance of R1?
In ideal case, if the IC is noiseless, we simply can choose R1<rs and problem is solved easy. However with an IC which generates noise as a 1000 ohm resistor, we can use R1 almost 500 ohm and despite R1>rs, this will not increase significant input noise.
If we build differential amplifier with PNP low noise transistors, this will increase current drain and noise in compariso with only one transistor
CONCLUSION: If we can compensate AIR and GND signals in input of RX, it is preferable to add a low noise preamp builded with only one PNP transistor.
The next question is:
How to design the resistance of RX coil for a low noise front end?

[mikebg]

RESISTANCE OF RX COIL

HOW TO DESIGN RESISTANCE OF RX COIL?

Increasing RX coil resistance we increase noise and bandwidth of its tuned LC circuit, but decrease the weight of RX winding and search head becomes more lightweight.
Let we analyse a situation when bandwidth BW depends only on Q factor of tuned RX coil. Above in posting #4 was given the formula for calculating the BW.
/1/ ________ BW=f/Q=r/(2пL)=0,16/T,
where
r and L are parameters of RX coil,
Q=2пfL/r is quality factor of RX coil, Q=2пf*T
and
/2/ ________ T=L/r
is timeconstant of RX coil.
Timeconstant of a coil is design parameter which determines its size, volume and weight (quantity of used metal for wire). From /1/ we obtain formula for calculating of design timeconstant:
/3/ ________T=0,16/BW.
For example, if we need the bandwidth of tuned RX coil to be BW=16Hz, we should design RX coil having design timeconstant T=0,16/BW=0,16/16=0,01s or 10ms. Such coil is not suitable for lightweight sensing head because need more metal, more volume and is too weighty.
From /2/ follows that resistance of RX coil is
/4/ _________ r=L/T.
The analysis shows that at given bandwidth BW, the design timeconstant T is given and we should use maximal possible inductance L to reduce weight of RX coil. An increased L is also good for sensitivity because more turns of RX winding means more voltage induced in RX coil and better S/N ratio. For maximal inductance we should use low equivalent capacitance of RX tank circuit. However in practice, the cable capacitance not allows to reduce equivalent tank capacitance below 900pF. Note that in WHITE'S RX tuned circuit, the capacitance is 15 times lesser than in TESORO RX tuned circuit. If the difference of capacitances was 16 times, we need 4 times more turns for RX coil, ie WHITE'S circuit receives near 4 times stronger RX signal or it has 12dB better S/N ratio if both circuits operate at equal TX frequency.
From calculation follows that we can not achieve necessery BW using only tuned RX coil. We need an additional LC tank having high Q as shown in above postings.
Let's design a RX coil for maximal S/N ratio in input. Because of minimal bandwidth of RX tank, it will generate minimal noise and receive minimum interferences.
DATA FOR CALCULATION
Given is TX frequency f=15kHz. To operate in wide temperatute range, we will increase bandwidth and calculate BW=16Hz for tuned RX coil, despite the target signal has maximum bandwidth about 4Hz. Let we use for calculation equivalent tank capacitance C=1nF as shown in WHITE'S patent for Coinmaster.
Calculation of coil inductance:
At given capacitance C of RX tank, for resonance we need inductance

/5/ ________ L=25,33E-3/(f^2.C)=25,33E-3/(15000^2.1E-9)=0,112H.

This is too large value despite the TX frequency is relative high.
Calculation of coil resistance:
From /1/ we obtain
/6/ _______ r=2п.BW.L=6,28.16.0,112= 11,2ohm.
CONCLUSIONS:
A) We calculated too small coil resistance for such large inductance 112mH, that means the RX coil will be too heavy. We should calculate the weight of metal and if coil is too weighty, we should increase bandwidth.
B) We calculated too small coil resistance relative to large noise resistance rbb'=50 ohm of used transistor.
C) From formula /3/ follows that design timeconstant of RX coil is independent on TX frequency and depends only on BW of tuned RX coil.
D) We need additional measures to realise lightweight RX coil for narrow band metal detector. One measure is to connect RX coil to Q-multiplier circuit, but this increases noise. Other measure is to connect in RFA an additional tuned LC circuit with high Q, for example using coil with potcore as shown in above postings.

At end of this analysis I should remember again that all circuit diagrams and calculations made in this thread are not so important nor suitable for a conventional metal detector for two resons:

1. The narrow bandwidth in input tank means steep phase characteristic. That causes not stabile discrimination and GND elimination of conventional metal detector, because reference voltage for synchronous demodulation is not extracted from RX signal, but from voltage across TX coil. For best results should be used the GND signal as reference.
2. The sensitivity of conventional metal detector is not limited by noise, but by large AIR and GND signals in input of RFA. To achieve maximal sensitivity, each metal detector should have two automatic controls: AGC and ABC, or 3 manual controls as shown in posting #7.
Two manual controls noted there as MAGNITUDE and PHASE, may be noted different as X and Y or as compensation of Real and Imaginery component.