audio transformerkamran/ee3202/lab1/f2_lab... · 2019-08-30 · electrical and computer engineering...

Electrical / Computer / Telecommunications Engineering

ELECTRICAL AND COMPUTER ENGINEERING FUNDAMENTALS LABS

Audio TransformerModelling and Testing



Transformers

• A transformer is a specific form of coupled circuit in which the coupling mechanism is the mutual inductance between the two coils

• The figure above is a general representation of an iron core transformer where the flux generated by the two currents will add with the currents in the direction shown

Typical construction of an iron core transformer. For clarity the coils are shown separately, but in the actual implementation one coil is wound around the other.



The Coupled Circuit Relationship

N1 N2

M

L1 L2

+

V1

-

I1

+

V2

-

I2

Transformers work by the mutual inductance between two coils of wire

For sinusoidal steady state waveforms the relationship between the currents and voltages show are:

𝑉𝑉1 = 𝑗𝑗𝜔𝜔𝐿𝐿1𝐼𝐼1 + 𝑗𝑗𝜔𝜔𝑗𝑗𝐼𝐼2

𝑉𝑉2 = 𝑗𝑗𝜔𝜔𝐿𝐿2𝐼𝐼2 + 𝑗𝑗𝜔𝜔𝑗𝑗𝐼𝐼1

An equivalent model for an ideal lossless transformer

La Lb

Lm

+

V1

-

I1

+

V2

-

I2 𝐿𝐿𝑎𝑎 = 𝐿𝐿1 − 𝑗𝑗

𝐿𝐿𝑏𝑏 = 𝐿𝐿2 − 𝑗𝑗

𝐿𝐿𝑚𝑚 = 𝐿𝐿1 + 𝑗𝑗



N1 N2

N1:N2

ZL

1:n+

V1

-

I1+

V2

-

I2

Z1

Ideal Iron Core Transformer

Ideal transformer relationships can be reduced to the turns ratios

𝑉𝑉2𝑉𝑉1

=𝑁𝑁2𝑁𝑁1

= 𝑛𝑛

𝐼𝐼2𝐼𝐼1

= −𝑁𝑁1𝑁𝑁2

= −1𝑛𝑛

𝑍𝑍1 =𝑍𝑍𝐿𝐿𝑛𝑛2



Ideal Audio Transformer – Step Down 11.5:1



Audio Transformer – Step Down 11.5:1• 8.2Ω resistor reflects back

through the transformer looking like a resistance of (11.5)2 (8.2Ω) = 1084Ω

• Signal generator therefore sees a 2084Ω load

• Resistor Rs and the reflection of RL act like a voltage divider giving a voltage across the transformer input of (1084/2084) Vg = 0.52 Vg



Real Audio Transformer – Model #1

Ra = Primary winding resistance Rb = secondary winding resistanceLa = primary leakage inductance Lb = secondary leakage inductanceCa = primary winding capacitance Cb = secondary winding capacitanceRm represents core losses (hysteresis and eddy current lossesLm = mutual inductance




Reflecting the secondary impedance back to the primary side, the model can be simplified

Rw = Ra + Rb/n2 and Lw = La + Lb/n2

Note that this model ignores the capacitance values and is intended for low frequencies




The values of the various components in this model can be measured with an RLC meter.

With the secondary shorted, the meter will give the values of Rw and Lw

With the secondary open, the meter will give the values of Rm and Lm (assuming they are large)



Real Audio Transformer – Step Down 11.5:1• Assuming some values close to those for the transformers to be used in this lab, the following model

is used



Real Audio Transformer – Step Down 11.5:1• Again taking account of the

8.2Ω resistor reflected back through the transformer the total impedance seen by the generator at 1000Hz has a magnitude of 1932Ω while the impedance across the transformer input has magnitude of 746Ω

• The voltage division then gives the input voltage of the transformer as (746/1932) Vg = 0.0.39 Vg



Real Audio Transformer – Step Down 11.5:1• If we analyze the frequency

response for this model we get the flat response characteristic show for low frequencies



Real Audio Transformer – Step Down 11.5:1• Analysis for a broader

frequency range gives



Real Audio Transformer – Step Down 11.5:1• Measurements on the real

transformer gave nice flat response for the under 5kHz range

• But the broader range measurements were different from the model showing some resonance effects associated with capacitance values in the real transformer that can be ignored at low frequencies

-60

-50

-40

-30

-20

-10

0

0 200 400 600 800 1000

V/Vg

en (

dB)

Fequency (kHz)

Frequency Response

Transformer Input Transformer Output



• At higher frequencies a different model is needed and will account for the resonance effect

• The value of Cr1 is found from the resonance with Lw. Assuming the resonance at 110kHz we get

• The value of Cr2 is smaller than Cr2 and produces some minor resonance effects at frequencies above 1MHz

Real Audio Transformer – High Frequency Model

𝑓𝑓 =1

2𝜋𝜋 𝐿𝐿𝑤𝑤𝐶𝐶𝑟𝑟𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑔𝑛𝑛𝑔𝑔 𝐶𝐶𝑟𝑟 =

12𝜋𝜋𝑓𝑓 2𝐿𝐿𝑤𝑤

= 523𝑝𝑝𝑝𝑝



Real Audio Transformer – HF Model 10kHz to 1MHz• This model shows the

resonance peak at 110kHz that matches the data recorded

• However it does not match the low frequency behavior

• The Low and High frequency models match at about 80kHz



Real Audio Transformer – HF Model• To adequately describe the real circuit operation, both models are required. Combining the response of the

two models gives results that match general trend of the the data recorded

audio transformerkamran/ee3202/lab1/f2_lab... · 2019-08-30 · electrical and computer engineering...

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