Minima

.. contents:: Table of Contents :depth: 3

Introduction

This document shall describe rationales used to design and build audio power amplifier using LM1875 integrated circuit.

Architecture

The amplifier architecture consists of the following sections:

• Input circuit
• Power amplifier
• Power supply

All sections are located on separate PCB boards.

.. image:: images/pcb_from_top.png

.. image:: images/pcb_render_corner.png

.. image:: images/pcb_render_from_top.png

Input circuit

The input circuit contains:

• Input EMI suppression

Input EMI suppression

To protect the input from EMI we will use the following Zobel network:

.. code:: o Positive input or negative input | | ----- Czi ----- | | +-+ Rzi | | | | +-+ | === Ground

For most input cables characteristic impedance falls in range between 50 and 100ohm impedance and we are using the 75ohm as the middle value. The resistor Rzi is Rzi=75ohm and the capacitor Czi is Czi=220pF. This network should be placed right at the input connector, not on the main amplifier PCB.

Also, a 100n X7R capacitor shall be placed between SGND and chassis right at the input connector. This capacitor will shunt radio and other interfirence signal into the Chassis Ground potential.

Power amplifier

• Input low pass filter
• The ground loop breaker resistor
• Output EMI suppression

Input low pass filter

For input filter we choose the frequency between 300kHz and 400kHz.

.. code::

    +---+ Rlp1    +---+ Rlp2
0---+   +----+----+   +---+---o Toward Amplifier IC block
    +---+    |    +---+   |
           ----- Clp1   ----- Clp2
           -----        -----
             |            |
            === Ground   === Ground

Using the 2nd order CR low-pass filter calculator at URL: http://sim.okawa-denshi.jp/en/CRCRtool.php we arrive at:

.. math::

Rlp1 = 100 Ohm, Rlp2 = 100 Ohm

Clp1 = 220pF,   Clp2 = 2.2nF

fp1 = 352kHz

fp2 = 14MHz

For more details please refer to: http://www.johnhearfield.com/RC/RC4.htm

The ground loop breaker resistor

A ground loop breaker resistor is located between SGND and GNDPWR grounds. The value of this resistor should be around 10 ohms.

Output EMI suppression

Output network consists of upstream and downstream Zobel Network and of output coil (Ld) with parallel, damping resistor (Rd). Upstream Zobel network provides a low-inductance load for the output stage at very high frequencies and allows high-frequency currents to circulate local to the output stage. The downstream Zobel network provides a good resistive termination right at the speaker terminals at high frequencies, helping to reduce RFI ingress and damp resonances with, or reflections from, the speaker cables. The output circuit is the following:

.. code::

Ld
         xxx
    +---x   x   x---+
    |        xxx    |
    |               |
    |   +-------+   |
o---+---|       |---+---o
Vout    +-------+   |   Vspeaker
    Rd              |
                  ----- Cz2 = 100nF
                  -----
                    |
                    |
                   +-+  Rz1 = 10 Ohm
                   | |
                   | |
                   +-+
                    |
                   ===

The output coil Ld provides high frequency isolation of output load from output stage of LM1875. The inductance value should be between 2uH up to 5uH. Output shunt resistor should be between 2 Ohm and 5 Ohms. See Douglas Self - Audio Power Amplifier Design Handbook, 3rd Ed., Output networks, chapter 7 for effect on power amplifier transfer function.

Power dissipation

NOTE:

• Maximum power dissipation should be around 25W per IC package for LM1875.

Fortunately, with music signals the power dissipation should be lower. Effective power of music signal is about 2 to 10 times as smaller than effective power of sinusoid signal. The power transformer is 200VA, meaning that each channel gets 100VA of power. Since the maximum output power at 8ohms is approximately 50W we get that the transformer supports crest factor of 4 (see: https://www.neurochrome.com/taming-the-lm3886-chip-amplifier/power-supply-design).

Gain value

For this power amplifier we are using non-inverting topology for simplicity reasons. If you would like to have less distortion then LM1875 should be used in inverting configuration.

The equivalent gain circuit resistance needs to stay below 600ohms. This is so because all noise measurements in data-sheet were done with 600ohms or 0ohms.

Using low feedback gain is preferred for several reasons:

• there is more loop gain available to reduce the distortion
• reduced output noise
• lower offset at output

Nominal gain is:

.. math::

G=-Rf/Rg+1

Using E24 series of resistors:

+-----------+-----------+---------+ | Rf [Ohm] | Rg [kOhm] | G [V/V] | +-----------+-----------+---------+ | 510 | 7.5 | 15.7 | +-----------+-----------+---------+ | 510 | 8.2 | 17.0 | +-----------+-----------+---------+ | 510 | 9.1 | 18.8 | +-----------+-----------+---------+ | 510 | 10.0 | 20.6 | +-----------+-----------+---------+ | 510 | 11.0 | 22.5 | +-----------+-----------+---------+

Using E48 series of resistors:

+-----------+-----------+---------+ | Rf [Ohm] | Rg [kOhm] | G [V/V] | +-----------+-----------+---------+ | 511 | 7.50 | 15.7 | +-----------+-----------+---------+ | 511 | 7.87 | 16.4 | +-----------+-----------+---------+ | 511 | 8.25 | 17.1 | +-----------+-----------+---------+ | 511 | 8.66 | 17.9 | +-----------+-----------+---------+ | 511 | 9.09 | 18.8 | +-----------+-----------+---------+ | 511 | 9.53 | 19.6 | +-----------+-----------+---------+ | 511 | 10.00 | 20.6 | +-----------+-----------+---------+ | 511 | 10.50 | 21.5 | +-----------+-----------+---------+ | 511 | 11.00 | 22.5 | +-----------+-----------+---------+ | 499 | 7.50 | 16.0 | +-----------+-----------+---------+

Chosen values for E24 series:

• Rf = 7.5kOhm
• Rg = 510 Ohm

Chosen values for E48 series:

• Rf = 7.5kOhm
• Rg = 499 Ohm

Frequency compensation

The LM1875 is modeled in the following way:

• Aol, typical open loop gain at DC.
• Fp1, dominant pole.
• Fp2, a pole which probably originates from output stage.
• Fp3, pole which probably originates from input or intermediate stages.
• Fp4 Hz, pole which probably originates from input or intermediate stages.
• Rops, open loop output stage impedance. The OPS open loop impedance is unusually low because the LM1875 uses output inclusive Miller compensation which can be observed on the equivalent schematic in the data-sheet.

+-----------+-----------+-----------+-----------+-----------+-----------+-----------+ | Chip | Aol [dB] | Fp1 [Hz] | Fp2 [Hz] | Fp3 [Hz] | Fp4 [Hz] | Rops [Ohm]| +-----------+-----------+-----------+-----------+-----------+-----------+-----------+ | LM1875 | 90 | 15 | 1.5e6 | 8e6 | 9e6 | 500e-3 | +-----------+-----------+-----------+-----------+-----------+-----------+-----------+

Lead compensation

Equivalent feedback network with lead compensation circuit::

          + Vout
          |
          *------+
          |      |
         +-+ Rf  |
         | |   ----- Cf=Cl (+Csi, see Input pin capacitance compensation)
         | |   -----
         +-+     |
   Vf     |      |
    +-----*------+
          |
         +-+ Rg
         | |
         | |
         +-+
          |
          + Input

Resistors `Rf` and `Rg` are part of feedback network. Capacitor `Cf` is the
compensation capacitor. The transfer function of this network is given as:

.. math::

Input pins have the following parasitic capacitances associated:

• Cdiff
• Cm
• Cstray

The LM1875 data-sheet does not specify any parameter regarding parasitic input capacitances. Voltage feedback OPAMPS usually have both differential and common-mode input impedances specified. In the absence of any information, it is safe to use the model given in the next figure:

.. code::

               +----+ Zdiff
+input o---+---|    |---+---o -input
           |   +----+   |
           |            |
          +-+ Zcm1     +-+ Zcm2
          | |          | |
          | |          | |
          +-+          +-+
           |            |
          ===          ===

We can use a rough estimation of values based on experience on using other audio BJT OPAMPS, and typical values are around Cdiff=5pF, Cm=4pF and Cstray=3pF. All three equivalent capacitors are tied in parallel, so the total input capacitance becomes:

.. math::

Cinput = Cdiff+Cm+Cstray=5pF+5pF+3pF=12pF

To mitigate this capacitance we can add capacitance Csi parallel to Rf resistor. To compensate for this the following equation is applied:

.. math::

Rf*Csi=Rg*Cinput

Csi=Cinput*Rg/Rf=0.8pF

Since we are already using lead compensation we just add this value to existing Cl capacitor.

Also, note that LM1875 model has tree more additional poles:

• Fp2, pole which probably originates from input or intermediate stages.
• Fp3, pole which probably originates from input or intermediate stages.
• A pole from Rops, open loop output stage impedance which in conjunction with output Zobel and connected load forms another high frequency pole.

Although all above poles are very high in frequency they still have their impact on lower frequency part of transfer function and reduce a few degrees of phase margin at UGBW point (approx. at 500kHz). Because of these poles we can freely put a bit bigger Cf capacitor value in the feedback network. Rough estimation is to put additional 1-3pF.

.. math::

Cadd = 2pF

For LM1875 we get:

.. math::

Cf=Cl+Csi+Cadd=14.1+0.8+2pF=16.9pF

Since the closest, standard values of capacitors are 15pF and 18pF, we choose the 15pF as the final value for Cl capacitor:

.. math::

Cf=15pF 

Power supply

Before rectifier diodes a snubber RC circuit should be placed to decrease diode switching impulse. Recommended values are Rsn = 1 Ohm, Csn = 470nF::

      o Vsupply
      |
      |
    ----- Csn = 470nF
    -----
      |
      |
     +-+  Rsn = 1 Ohm
     | |
     | |
     +-+
      |
     === Ground

This snubber may be placed near the IC power supply lines, too.

Using stabilized power supplies, for example by using LT1083 regulator is only meaningful at lower output powers. The regulation becomes really expensive when used in high power amplifiers. Regulated power supplies are OK when used up to powers of 20W-30W @ 8 Ohm.

NOTE:

• On case chassis there should be a safety ground screw just near at the input 220V socket.

Transformer specification for LM1875 amplifier is the following:

• S=80VA, power rating.
• Usn1=18Veff, first secondary nominal voltage.
• Usn2=18Veff, second secondary nominal voltage.
• k=10%, regulation.

Secondary internal resistance is:

.. math::

Usu=Usn1*(1+(k/100))

Isn=S/(Usn1+Usn2)

Ri=(Usn1-Usu)/Isn

Using values from above we get:

.. math::

Usu=18*(1+(10/100))=19.8Veff

Isn=2.2Aeff

Ri=810mOhm

The power supply section is using single banks of 10mF capacitors with 0.22Ohm resistor in series between bridge rectifier and smoothing capacitors.