How can a 50 ohm resistor be used to produce reference signal on a radio telescope with 50 ohm impedance? Surely, resistance and impedance are not the same thing.

[Andrew Thornett]

This is one of those radio-astronomy tricks that feels almost too simple until you see why it works.

The key idea

A 50 Ω resistor at a known temperature is a predictable noise source.

If your radio telescope (LNA, receiver chain, backend) also has a 50 Ω input impedance, then a 50 Ω resistor connected to that input is a perfectly matched thermal noise source. No reflections, no standing waves — just clean, well-defined noise power.

---

What the resistor actually produces

Any resistor above absolute zero generates Johnson–Nyquist noise. The available noise power is

P = k T B

where:

• k = Boltzmann’s constant
• T = physical temperature of the resistor (Kelvin)
• B = receiver bandwidth (Hz)

Crucially:

• The resistance value doesn’t change the noise power, as long as it is impedance-matched
• A 50 Ω resistor into a 50 Ω system delivers maximum available noise power

---

Why this is useful for a radio telescope

When you switch your receiver input from the antenna to a 50 Ω load:

• The sky signal disappears
• You see a stable, known noise temperature
• That becomes a reference level for calibration

This is the basis of:

• Y-factor measurements
• System temperature (Tsys) determination
• Gain calibration
• Drift monitoring

---

Practical implementations

1. Ambient “cold” reference

A simple 50 Ω terminator at room temperature:

• T approx. 290 K.
• Acts as a known cold load
• Used to establish baseline receiver noise

2. Heated “hot” reference

The same resistor, deliberately heated:

• 400–600 K (or more)
• Gives a second reference point
• Enables absolute calibration

3. Noise diode equivalent

A calibrated noise diode is essentially:

• A controlled broadband noise source
• Designed to look like a hot 50 Ω resistor

---

Why impedance matching matters so much

If the resistor were not 50 Ω:

• Reflections would occur
• Noise power at the receiver would be frequency-dependent
• Calibration would be unreliable

With a matched 50 Ω load:

• All generated noise is absorbed by the receiver
• The reference is spectrally flat
• Calibration becomes clean and repeatable

---

In telescope terms

Think of the 50 Ω resistor as an artificial sky with a precisely known brightness temperature.

Switching between:

• Antenna → real sky
• 50 Ω load → known sky

lets you translate raw power levels into Kelvin, which is what radio astronomy actually cares about.

---

I don't understand how 50 ohm resistor matches 50 ohm impedance- surely the two are not the same thing?

You’re absolutely right to be suspicious here — the wording sounds hand-wavy until the distinction is nailed down properly. Let’s slow it right down and separate the concepts.

---

Resistance vs impedance (the clean separation)

• Resistance (R)
  A real, dissipative property. Converts RF power into heat. A 50 Ω resistor is (ideally) frequency-independent.

• Impedance (Z)
  The ratio of RF voltage to current at a port:

  Z = V / I

So yes — they are not the same thing in general.

---

Why they are equivalent here

When we say:

“a 50 Ω resistor matches a 50 Ω system”

what we really mean is:

The input impedance of the receiver is designed to be 50 Ω resistive, and the resistor presents 50 Ω resistive impedance at the frequencies of interest.

If both sides present:

Z = 50 + j0Ω

then from the RF signal’s point of view:

• Voltage and current ratios match
• No reflections occur
• Maximum available power is transferred

At that point, the distinction stops mattering electrically.

---

Think in terms of ports, not components

At RF we don’t think “this is a resistor” or “this is an amplifier”. We think:

What impedance does this port present at this frequency?

• A receiver input is engineered to look like a 50 Ω resistor
• A termination resistor is physically a 50 Ω resistor

If both ports look identical to the wave, they are matched — regardless of what’s inside.

---

Why the receiver isn’t a “real” resistor

Good instinct again.

The receiver input:

• Does not dissipate all power as heat
• May feed a transistor gate or mixer
• Uses matching networks to transform the internal device impedance to 50 Ω

But at the input connector:

• The effective impedance is still 50 Ω
• The wave doesn’t “know” what happens after that point

That’s all matching ever means.

---

Where people get tripped up

The sloppy phrase:

“50 Ω resistor matches 50 Ω impedance”

really means:

“Two ports present equal complex impedance, so no reflection occurs”

It has nothing to do with:

• DC behaviour
• What the device internally does
• Whether energy becomes heat or signal processing

---

Why this matters for noise calibration

Thermal noise theory assumes:

• A resistive source
• A matched load

When your receiver input is matched:

• Exactly half the noise voltage appears across the load
• The available noise power is
• That is what makes the resistor a calibrated noise source

---

One last intuition

Imagine shouting down a perfectly tuned hallway:

• If the walls and air impedance match your voice → no echo
• If they don’t → reflections

The hallway doesn’t have to be “made of your throat” — it just has to present the same impedance.

---

[Alex P]

https://www.k3emd.com/downloads/Reflect.pdf

Instead of relying upon questionable AI answers .. Read a Book !

[Andrew Thornett]

So Alex is the AI wrong? If so in what way. 

Andy

Sent from Outlook for Android

---

From: 'Alex P' via Society of Amateur Radio Astronomers <sara...@googlegroups.com>
Sent: Thursday, February 5, 2026 6:05:26 AM
To: Society of Amateur Radio Astronomers <sara...@googlegroups.com>
Subject: [SARA] Re: How can a 50 ohm resistor be used to produce reference signal on a radio telescope with 50 ohm impedance? Surely, resistance and impedance are not the same thing.

 

https://www.k3emd.com/downloads/Reflect.pdf

Instead of relying upon questionable AI answers .. Read a Book !

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[b alex pettit jr]

The Issue I have with " AI " is that unless the information set from which the data is extracted is Known or someway Limited,

How do you know it is Valid ? 

 There's lots of strange stuff on the INTERNET !

======================================================================

[andrew....@googlemail.com]

Hi Alex,

In that you are absolutely right – I have noticed that when I ask questions of ChatGPT sometimes it quotes my own website www.astronomy.me.uk – now that is a really dubious source of information – I know what rubbish is on there – but it turns out that 100+ GB of apparently sensible information with top level URL seems to persuade the AI engine that this is good quality information!

NB For anyone reading my website please let me know where information is wrong and needs to be changed or put comment to that effect on the webpage in question.

Andy

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[b alex pettit jr]

Hi Andrew,

I'm not saying the info in the post is incorrect, just that some of it is 'strange' ?

 No amateur radio operator has a perfect Z = 50 + j0 Ohm impedance amplifier output, cable, and antenna system, 

    but they do not have 'echos' on their voice when they talk.

Alex

=======================================================================

[andrew....@googlemail.com]

That is helpful to know – please keep such comments coming along!

 

From: 'b alex pettit jr' via Society of Amateur Radio Astronomers <sara...@googlegroups.com>
Sent: 05 February 2026 10:58
To: andrew.thornett via Society of Amateur Radio Astronomers <sara...@googlegroups.com>
Subject: Re: [SARA] Re: How can a 50 ohm resistor be used to produce reference signal on a radio telescope with 50 ohm impedance? Surely, resistance and impedance are not the same thing.

 

Hi Andrew,

=======================================================================

 

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[b alex pettit jr]

 ''Reflections' in the coax, etc do exist ( the SWR ratio ) and there can be significant amounts of power temporarily stored

in the Reactance of the mismatch.  BUT, information in RF frequency systems is contained in the change of the signal strength or frequency.

SO, although the coax might 'sound' like an acoustic echo chamber, it has no meaning with Signal Quality . Loss Yes.

= an example of an Automated Information retrieval system .. it has a huge data base, but no Brains :)

 

[bsn...@gmail.com]

Without getting into this discussion,  the last and latest version of Reflections, Reflections III, is available here:

https://old.w1yca.org › tech › ant › reflectIII.pdf

There are many of changes and clarifications that probably make this worth a look...

Really like this:  = an example of an Automated Information retrieval system .. it has a huge data base, but no Brains :) TNX

....bill....

[Stephen Arbogast]

Yes,    resistance  and impedance are not the  same as is taught in  Electrical  Engineering.  Always  two  components  to  consider  in  formal  circuit analysis. .  Resistance refers  to   energy  loss due to heat.  Impedance refers  to  inductance  and  capacitance  reactance.  Normally  we treat a  50 ohm  resistor  as something  that looses  energy due to heat.  Inductors  and capacitors   store energy  in magnetic  and  electric  fields.   All  passive  components  exhibit  all  three  but  depending  on the model that  suits  our engineering    problem we choose to ignore either  resistance or  reactance.  

For  an  antenna   I  don't thing  it would  be a good idea  to  ignore  inductive  and  capacitor  reactance when  considering  reflected power.    It works  both ways  due to  reciprocity  theorem.  This why  we use  NanoVNA   to measure  impedance . I have heard comments  from ham radio  videos that for receiving  .....  a good impedance  match  between  antenna and  receiver is not important.   This  is false... it works  both ways.   Also  an antenna tuned to resonance does not  guarantee a  good match.. this  means  the  inductance  and capacitor reactance   cancel   but  maybe  the  resistances  don't match.

[Stephen Arbogast]

QSpice  is a  very  good  circuit  simulator  but  only on Windows....    https://www.qorvo.com/design-hub/design-tools/interactive/qspice#requirements

[tedcl...@gmail.com]

        On Thursday, February 5, 2026 at 3:56:02 PM UTC-7 bsn...@gmail.com wrote:

          Without getting into this discussion,  the last and latest version of Reflections, Reflections III, is available here:
          https://old.w1yca.org › tech › ant › reflectIII.pdf

https://old.w1yca.org/tech/ant/reflectIII.pdf

Thanks !

[Stephen Arbogast]

This is  very  cool!   In the   1960's  in  high   school I was taught about  SWR in  amateur  radio but  later  learned  it  is   reflected  power   in  EE  at  University  of  Colorado .  As  Festus on  Gun Smoke would  say  to  Doc   Adams  You old  scudder   just   say  what  you mean.  I   prefer  the   Physics    stuff     Is it e^i*omega*t   or  e^j*omega* t    ?

[Stephen Arbogast]

Some  thoughts  about   my   time  on  two   aircraft  carriers during   Vietnam..    I was  never officially in   the Navy     but  I did   spend time, early  70's, on    the   Nimitz   and  Kitty  Hawk aircraft  carriers working  for  Hughes  Aircraft. My  job was in  the TSC, Tactical  Support  Center making  sure data   was being transferred  from    various   sensors  via   8 bit   micro  controllers to   a  tactical/tabular     display.....  We   complained then that  data  transfer was  slow from   sono-buoys    dropped   from  P3   aircraft ...   the data transfer  was  very   slow but  it  worked.....