Mastering Electronics Design

7/25/2019 Mastering Electronics Design

1/14

6/23/2016 Master ingElectronicsDesign.com : How to Der ive the RMS Value of a Sine Wave wi th a DC Offset

http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/

Mastering Electronics Design

Visit Mastering

Electronics Design

page on Facebook

and on NetworkedBlogs

124 Followers so far

Related Posts

1. How to Derive the RMS Value of Pulse and Square Waveforms

2. How to Derive the RMS Value of a Trapezoidal Waveform Part 1

3. How to Derive the RMS Value of a Triangle Waveform

4. How to Calculate the RMS Value of an Arbitrary Waveform

Books I recommend

Data Conversion

Handbook

Anal og Devi ces Inc...

Privacy Information

My comment: Great book to learn ADCs and DACs from the people who design them at Analog Devices. It covers the ADCs and DACs

technologies, how t o choose them for your design, and explains in detail their specifications.

Click to see another bookor

Check the full list here
http://www.amazon.com/dp/0750678410/ref=as_sl_pc_tf_lc?tag=theartofelede-20&camp=213381&creative=390973&linkCode=as4&creativeASIN=0750678410&adid=1714Q6J3MGVZNGV9Q9QE&&ref-refURL=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fwp-content%2Fscript%2Famstore2.phphttp://www.amazon.com/dp/0750678410/ref=as_sl_pc_tf_lc?tag=theartofelede-20&camp=213381&creative=390973&linkCode=as4&creativeASIN=0750678410&adid=1714Q6J3MGVZNGV9Q9QE&&ref-refURL=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fwp-content%2Fscript%2Famstore2.phphttp://www.amazon.com/dp/0750678410/ref=as_sl_pc_tf_lc?tag=theartofelede-20&camp=213381&creative=390973&linkCode=as4&creativeASIN=0750678410&adid=1714Q6J3MGVZNGV9Q9QE&&ref-refURL=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fwp-content%2Fscript%2Famstore2.phphttp://masteringelectronicsdesign.com/books-i-recommend/http://www.amazon.com/gp/dra/infohttp://www.amazon.com/dp/0750678410/ref=as_sl_pc_tf_lc?tag=theartofelede-20&camp=213381&creative=390973&linkCode=as4&creativeASIN=0750678410&adid=1714Q6J3MGVZNGV9Q9QE&&ref-refURL=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fwp-content%2Fscript%2Famstore2.phphttp://www.amazon.com/dp/0750678410/ref=as_sl_pc_tf_lc?tag=theartofelede-20&camp=213381&creative=390973&linkCode=as4&creativeASIN=0750678410&adid=1714Q6J3MGVZNGV9Q9QE&&ref-refURL=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fwp-content%2Fscript%2Famstore2.phphttp://masteringelectronicsdesign.com/how-to-calculate-the-rms-value-of-an-arbitrary-waveform/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-triangle-waveform/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-trapezoidal-waveform/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-pulse-and-square-waveforms/http://networkedblogs.com/blog/mastering_electronics_design/http://facebook.com/masteringelectronicsdesign/http://networkedblogs.com/blog/mastering_electronics_design/http://masteringelectronicsdesign.com/


2/14


http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/ 2

Useful Electronics Links

SPICE Links

Semiconductor Manufacturers

Electronics Forums

Notable Articles in Electronics Design

You may also be interested in

Build an Op Amp SPICE Model from Its Datasheet - Part 3

Design a Differential Amplifier the Easy Way with Mathcad

Why this website?

The RMS Value of a Trapezoidal Waveform Part 2

Build an Op Amp SPICE Model from Its Datasheet - Part 2

Why do I do this?

Using the Summing Amplifier as an Average Amplifier

Bipolar to Unipolar Converters Based on a Summing Amplifier Configuration

ROHM/SiC PowerModule

1200V/180A-

rated SiCMOS

module SW

frequencies

over 50kHz

supported

RMS

Sine Wave

Square Root

Ads byGoogle
http://masteringelectronicsdesign.com/bipolar-to-unipolar-converter-examples/http://masteringelectronicsdesign.com/build-an-op-amp-spice-model-from-its-datasheet-part-2/http://masteringelectronicsdesign.com/design-a-differential-amplifier-the-easy-way-with-mathcad/https://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-8096656746985808&output=html&h=90&slotname=0815705272&adk=675553154&w=160&lmt=1466695377&flash=22.0.0&url=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&wgl=1&dt=1466695376586&bpp=50&bdt=1563&fdt=1026&idt=1173&shv=r20160617&cbv=r20151006&saldr=aa&prev_fmts=160x90_0ads_al&correlator=7449671652583&frm=20&ga_vid=*&ga_sid=*&ga_hid=*&ga_fc=0&ga_wpids=UA-8631654-1&pv=1&iag=3&icsg=2&nhd=1&dssz=2&mdo=0&mso=0&u_tz=330&u_his=1&u_java=0&u_h=768&u_w=1024&u_ah=738&u_aw=1024&u_cd=24&u_nplug=5&u_nmime=7&dff=lucida%20grande&dfs=11&biw=1007&bih=634&eid=575144605&ref=https%3A%2F%2Fwww.google.co.in%2F&rx=0&eae=0&fc=80&pc=1&brdim=0%2C0%2C0%2C0%2C1024%2C0%2C1024%2C738%2C1024%2C634&vis=1&rsz=%7C%7C%7C&abl=CS&ppjl=t&pfx=0&fu=16&bc=1&ifi=2&xpc=FRtOLyYzpM&p=http%3A//masteringelectronicsdesign.com&dtd=1323&rl_rc=true&adsense_enabled=true&ad_type=text&oe=utf8&format=fpkc_al_lp&fs=small&f=verdana&kw_type=radlink&hl=en&kw0=RMS&kw1=Sine+Wave&kw2=Square+Root&okw=Sine+Wave&rt=ChBXa_6xAAWqnwpon8sKAX13EglTaW5lIFdhdmUaCAhZsLe6tfO2KAFSEwiY96_4ub7NAhWTimgKHZLdCj0http://masteringelectronicsdesign.com/electronics-forums/http://masteringelectronicsdesign.com/spice-links/http://masteringelectronicsdesign.com/why-do-i-do-this/http://masteringelectronicsdesign.com/build-an-op-amp-spice-model-from-its-datasheet-part-2/https://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-8096656746985808&output=html&h=90&slotname=0815705272&adk=675553154&w=160&lmt=1466695377&flash=22.0.0&url=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&wgl=1&dt=1466695376586&bpp=50&bdt=1563&fdt=1026&idt=1173&shv=r20160617&cbv=r20151006&saldr=aa&prev_fmts=160x90_0ads_al&correlator=7449671652583&frm=20&ga_vid=*&ga_sid=*&ga_hid=*&ga_fc=0&ga_wpids=UA-8631654-1&pv=1&iag=3&icsg=2&nhd=1&dssz=2&mdo=0&mso=0&u_tz=330&u_his=1&u_java=0&u_h=768&u_w=1024&u_ah=738&u_aw=1024&u_cd=24&u_nplug=5&u_nmime=7&dff=lucida%20grande&dfs=11&biw=1007&bih=634&eid=575144605&ref=https%3A%2F%2Fwww.google.co.in%2F&rx=0&eae=0&fc=80&pc=1&brdim=0%2C0%2C0%2C0%2C1024%2C0%2C1024%2C738%2C1024%2C634&vis=1&rsz=%7C%7C%7C&abl=CS&ppjl=t&pfx=0&fu=16&bc=1&ifi=2&xpc=FRtOLyYzpM&p=http%3A//masteringelectronicsdesign.com&dtd=1323&rl_rc=true&adsense_enabled=true&ad_type=text&oe=utf8&format=fpkc_al_lp&fs=small&f=verdana&kw_type=radlink&hl=en&kw0=RMS&kw1=Sine+Wave&kw2=Square+Root&okw=Square+Root&rt=ChBXa_6xAAWqoQpon8sKAX13EgtTcXVhcmUgUm9vdBoI2tnMRcy91L0oAVITCJj3r_i5vs0CFZOKaAodkt0KPQhttps://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-8096656746985808&output=html&h=90&slotname=0815705272&adk=675553154&w=160&lmt=1466695377&flash=22.0.0&url=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&wgl=1&dt=1466695376586&bpp=50&bdt=1563&fdt=1026&idt=1173&shv=r20160617&cbv=r20151006&saldr=aa&prev_fmts=160x90_0ads_al&correlator=7449671652583&frm=20&ga_vid=*&ga_sid=*&ga_hid=*&ga_fc=0&ga_wpids=UA-8631654-1&pv=1&iag=3&icsg=2&nhd=1&dssz=2&mdo=0&mso=0&u_tz=330&u_his=1&u_java=0&u_h=768&u_w=1024&u_ah=738&u_aw=1024&u_cd=24&u_nplug=5&u_nmime=7&dff=lucida%20grande&dfs=11&biw=1007&bih=634&eid=575144605&ref=https%3A%2F%2Fwww.google.co.in%2F&rx=0&eae=0&fc=80&pc=1&brdim=0%2C0%2C0%2C0%2C1024%2C0%2C1024%2C738%2C1024%2C634&vis=1&rsz=%7C%7C%7C&abl=CS&ppjl=t&pfx=0&fu=16&bc=1&ifi=2&xpc=FRtOLyYzpM&p=http%3A//masteringelectronicsdesign.com&dtd=1323&rl_rc=true&adsense_enabled=true&ad_type=text&oe=utf8&format=fpkc_al_lp&fs=small&f=verdana&kw_type=radlink&hl=en&kw0=RMS&kw1=Sine+Wave&kw2=Square+Root&okw=Sine+Wave&rt=ChBXa_6xAAWqnwpon8sKAX13EglTaW5lIFdhdmUaCAhZsLe6tfO2KAFSEwiY96_4ub7NAhWTimgKHZLdCj0https://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-8096656746985808&output=html&h=90&slotname=0815705272&adk=675553154&w=160&lmt=1466695377&flash=22.0.0&url=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&wgl=1&dt=1466695376586&bpp=50&bdt=1563&fdt=1026&idt=1173&shv=r20160617&cbv=r20151006&saldr=aa&prev_fmts=160x90_0ads_al&correlator=7449671652583&frm=20&ga_vid=*&ga_sid=*&ga_hid=*&ga_fc=0&ga_wpids=UA-8631654-1&pv=1&iag=3&icsg=2&nhd=1&dssz=2&mdo=0&mso=0&u_tz=330&u_his=1&u_java=0&u_h=768&u_w=1024&u_ah=738&u_aw=1024&u_cd=24&u_nplug=5&u_nmime=7&dff=lucida%20grande&dfs=11&biw=1007&bih=634&eid=575144605&ref=https%3A%2F%2Fwww.google.co.in%2F&rx=0&eae=0&fc=80&pc=1&brdim=0%2C0%2C0%2C0%2C1024%2C0%2C1024%2C738%2C1024%2C634&vis=1&rsz=%7C%7C%7C&abl=CS&ppjl=t&pfx=0&fu=16&bc=1&ifi=2&xpc=FRtOLyYzpM&p=http%3A//masteringelectronicsdesign.com&dtd=1323&rl_rc=true&adsense_enabled=true&ad_type=text&oe=utf8&format=fpkc_al_lp&fs=small&f=verdana&kw_type=radlink&hl=en&kw0=RMS&kw1=Sine+Wave&kw2=Square+Root&okw=RMS&rt=ChBXa_6xAAWqjwpon8sKAX13EgNSTVMaCD84KEAH5pJKKAFSEwiY96_4ub7NAhWTimgKHZLdCj0https://googleads.g.doubleclick.net/aclk?sa=L&ai=CaTZGsP5rV7L0IsWloAPl_6HQAeK5kIhFgtW2z_cCwI23ARABIOGigBVg5YKAgNwpyAEBqQJ43RaKmlBEPqgDAcgDwwSqBM4BT9D-gO_ayAkTpgH2ClPpCG8Cf-U5Wb3QvcFU2kMRbZkgUYmKS2rjXTjSzM79FIjNe9zWW9oRHF8rMRLYB_4oiLuD6LoQTfIVEqEMuigJv5hpgfW2RoZSCcQUVUmJXVg2H0j-05xNSNt5waY8E9s2gL1JGG_s9H8wHiQLQVcEvdKZP-oRTLmXWLH2FlENnYKxpfEcACErfEX2AgqHIZRvIhxGqOxhbxOsnBiN27Rv8_XZckd4G86wcpdlFVSOLz_w4KpFM3Nw2epzIq4Kq1SAB8r8lUmoB6a-G9gHAQ&num=1&sig=AOD64_3PE_LcYIVqRoJP356nL2mckUUIIQ&client=ca-pub-8096656746985808&adurl=http://www.rohm.com/web/in/products/-/product/BSM180D12P2C101https://googleads.g.doubleclick.net/aclk?sa=L&ai=CaTZGsP5rV7L0IsWloAPl_6HQAeK5kIhFgtW2z_cCwI23ARABIOGigBVg5YKAgNwpyAEBqQJ43RaKmlBEPqgDAcgDwwSqBM4BT9D-gO_ayAkTpgH2ClPpCG8Cf-U5Wb3QvcFU2kMRbZkgUYmKS2rjXTjSzM79FIjNe9zWW9oRHF8rMRLYB_4oiLuD6LoQTfIVEqEMuigJv5hpgfW2RoZSCcQUVUmJXVg2H0j-05xNSNt5waY8E9s2gL1JGG_s9H8wHiQLQVcEvdKZP-oRTLmXWLH2FlENnYKxpfEcACErfEX2AgqHIZRvIhxGqOxhbxOsnBiN27Rv8_XZckd4G86wcpdlFVSOLz_w4KpFM3Nw2epzIq4Kq1SAB8r8lUmoB6a-G9gHAQ&num=1&sig=AOD64_3PE_LcYIVqRoJP356nL2mckUUIIQ&client=ca-pub-8096656746985808&adurl=http://www.rohm.com/web/in/products/-/product/BSM180D12P2C101http://masteringelectronicsdesign.com/bipolar-to-unipolar-converter-examples/http://masteringelectronicsdesign.com/using-the-summing-amplifier-as-an-average-amplifier/http://masteringelectronicsdesign.com/why-do-i-do-this/http://masteringelectronicsdesign.com/build-an-op-amp-spice-model-from-its-datasheet-part-2/http://masteringelectronicsdesign.com/the-rms-value-of-a-trapezoidal-waveform-part-2/http://masteringelectronicsdesign.com/why-this-website/http://masteringelectronicsdesign.com/design-a-differential-amplifier-the-easy-way-with-mathcad/http://masteringelectronicsdesign.com/build-an-op-amp-spice-model-from-its-datasheet-part-3/http://masteringelectronicsdesign.com/notable-articles-in-electronics-design/http://masteringelectronicsdesign.com/electronics-forums/http://masteringelectronicsdesign.com/semiconductor-manufacturers/http://masteringelectronicsdesign.com/spice-links/


3/14



Sites I follow

EDN Design Ideas

Analog Devices

New Products at Texas Instruments

Linear Technology Corporation

EEWeb

Electronic Products

How to Derive the RMS Value of a Sine Wave with a DC Offset

by Adrian S. Nastase

Email 45 Comments Print Subscribe

I noticed a question posted on one of Yahoos Q&A sites, asking what is the RMS value of a sine wave with a DC offset. The chosen

answer as being the best was actually wrong. The next comment, which was trying to correct the best answer, was wrong too. I am

not going to post the Yahoo link here. What I can do, is to show how to derive the RMS value of such waveform.

Lets derive first the RMS value of a sine wave with no DC offset

Lets start with the RMS value of a sine wave, with no DC offset, which is shown in Figure 1. It is well known that the RMS value of a

sine wave is 0.707 times the signal peak level, but how can you prove this?

Figure 1

As shown in this article, MasteringElectronicsDesign.com: How to Derive the RMS Value of a Trapezoidal Waveform, or other RMS

articles in this website, lets start with the RMS definition.

True RMS Meter

Derive 5

Offset Offset

Ads byGoogle
https://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-8096656746985808&output=html&h=90&slotname=4903007605&adk=2047241228&w=180&lmt=1466695378&flash=22.0.0&url=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&wgl=1&dt=1466695376637&bpp=16&bdt=1614&fdt=1831&idt=1845&shv=r20160617&cbv=r20151006&saldr=aa&prev_fmts=180x90_0ads_al&prev_slotnames=0815705272&correlator=7449671652583&frm=20&ga_vid=*&ga_sid=*&ga_hid=*&ga_fc=1&ga_wpids=UA-8631654-1&pv=1&iag=3&icsg=2&nhd=1&dssz=2&mdo=0&mso=0&u_tz=330&u_his=1&u_java=0&u_h=768&u_w=1024&u_ah=738&u_aw=1024&u_cd=24&u_nplug=5&u_nmime=7&dff=lucida%20grande&dfs=11&biw=1007&bih=634&eid=575144605&ref=https%3A%2F%2Fwww.google.co.in%2F&rx=0&eae=0&fc=80&pc=1&brdim=0%2C0%2C0%2C0%2C1024%2C0%2C1024%2C738%2C1024%2C634&vis=1&rsz=%7C%7C%7C&abl=CS&ppjl=t&pfx=0&fu=16&bc=1&ifi=3&xpc=OnlyPR9oci&p=http%3A//masteringelectronicsdesign.com&dtd=1970&rl_rc=true&adsense_enabled=true&ad_type=text&oe=utf8&format=fpkc_al_lp&fs=small&f=verdana&kw_type=radlink&hl=en&kw0=True+RMS+Meter&kw1=Derive+5&kw2=Offset+Offset&okw=Offset+Offset&rt=ChBXa_6xAA8LEQpoJIF2B2KDEg1PZmZzZXQgT2Zmc2V0Ggg7nRkj3c1xdygBMAJSEwiKr9n4ub7NAhVOE2gKHbjOBZ8https://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-8096656746985808&output=html&h=90&slotname=4903007605&adk=2047241228&w=180&lmt=1466695378&flash=22.0.0&url=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&wgl=1&dt=1466695376637&bpp=16&bdt=1614&fdt=1831&idt=1845&shv=r20160617&cbv=r20151006&saldr=aa&prev_fmts=180x90_0ads_al&prev_slotnames=0815705272&correlator=7449671652583&frm=20&ga_vid=*&ga_sid=*&ga_hid=*&ga_fc=1&ga_wpids=UA-8631654-1&pv=1&iag=3&icsg=2&nhd=1&dssz=2&mdo=0&mso=0&u_tz=330&u_his=1&u_java=0&u_h=768&u_w=1024&u_ah=738&u_aw=1024&u_cd=24&u_nplug=5&u_nmime=7&dff=lucida%20grande&dfs=11&biw=1007&bih=634&eid=575144605&ref=https%3A%2F%2Fwww.google.co.in%2F&rx=0&eae=0&fc=80&pc=1&brdim=0%2C0%2C0%2C0%2C1024%2C0%2C1024%2C738%2C1024%2C634&vis=1&rsz=%7C%7C%7C&abl=CS&ppjl=t&pfx=0&fu=16&bc=1&ifi=3&xpc=OnlyPR9oci&p=http%3A//masteringelectronicsdesign.com&dtd=1970&rl_rc=true&adsense_enabled=true&ad_type=text&oe=utf8&format=fpkc_al_lp&fs=small&f=verdana&kw_type=radlink&hl=en&kw0=True+RMS+Meter&kw1=Derive+5&kw2=Offset+Offset&okw=Derive+5&rt=ChBXa_6xAA8LDwpoJIF2B2KDEghEZXJpdmUgNRoICaBU4dHuGoAoATACUhMIiq_Z-Lm-zQIVThNoCh24zgWfhttps://googleads.g.doubleclick.net/pagead/ads?client=ca-pub-8096656746985808&output=html&h=90&slotname=4903007605&adk=2047241228&w=180&lmt=1466695378&flash=22.0.0&url=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&wgl=1&dt=1466695376637&bpp=16&bdt=1614&fdt=1831&idt=1845&shv=r20160617&cbv=r20151006&saldr=aa&prev_fmts=180x90_0ads_al&prev_slotnames=0815705272&correlator=7449671652583&frm=20&ga_vid=*&ga_sid=*&ga_hid=*&ga_fc=1&ga_wpids=UA-8631654-1&pv=1&iag=3&icsg=2&nhd=1&dssz=2&mdo=0&mso=0&u_tz=330&u_his=1&u_java=0&u_h=768&u_w=1024&u_ah=738&u_aw=1024&u_cd=24&u_nplug=5&u_nmime=7&dff=lucida%20grande&dfs=11&biw=1007&bih=634&eid=575144605&ref=https%3A%2F%2Fwww.google.co.in%2F&rx=0&eae=0&fc=80&pc=1&brdim=0%2C0%2C0%2C0%2C1024%2C0%2C1024%2C738%2C1024%2C634&vis=1&rsz=%7C%7C%7C&abl=CS&ppjl=t&pfx=0&fu=16&bc=1&ifi=3&xpc=OnlyPR9oci&p=http%3A//masteringelectronicsdesign.com&dtd=1970&rl_rc=true&adsense_enabled=true&ad_type=text&oe=utf8&format=fpkc_al_lp&fs=small&f=verdana&kw_type=radlink&hl=en&kw0=True+RMS+Meter&kw1=Derive+5&kw2=Offset+Offset&okw=True+RMS+Meter&rt=ChBXa_6xAA8K_gpoJIF2B2KDEg5UcnVlIFJNUyBNZXRlchoI79Qcw9-rPF0oATACUhMIiq_Z-Lm-zQIVThNoCh24zgWfhttp://masteringelectronicsdesign.com/tag/rms/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-trapezoidal-waveform/http://masteringelectronicsdesign.com/wp-content/uploads/2012/02/sine-wave-zero-offset.pnghttp://feeds.feedburner.com/MasteringElectronicsDesignmailto:?subject=How%20to%20Derive%20the%20RMS%20Value%20of%20a%20Sine%20Wave%20with%20a%20DC%20Offset&body=http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/https://www.addtoany.com/share#url=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&title=MasteringElectronicsDesign.com%20%3A%20How%20to%20Derive%20the%20RMS%20Value%20of%20a%20Sine%20Wave%20with%20a%20DC%20Offset&description=This%20article%20shows%20how%20to%20derive%20the%20RMS%20value%20of%20a%20sine%20wave%20with%20DC%20offset.http://www.electronicproducts.com/http://www.eeweb.com/http://www.linear.com/products/http://focus.ti.com/general/docs/newproducts.tsp?releasePeriod=179&x=19&y=12&contentType=3http://www.analog.com/http://www.edn.com/channel/Design_Ideas.php


4/14



(1)

The sine wave time dependency can be described by the following function:

(2)

T is the function period, or T = 1/f where f is the waveform frequency. Also, a1is the amplitude.

Replacing (2) in (1), and calculating the integral over a full period T, we find the RMS value squared as in the following equation:

(3)

The standard method to calculate a squared sine integral is to transform it into its double angle equivalent, using a trigonometric identity

usually called the power-reduction formula.

(4)

So the RMS squared becomes

(5)

If youre wandering why the sine term is zero in the previous equation, thats because

(6)

Therefore, the RMS value of a sine wave with offset zero is the following well known formula,

(7)

The RMS Value of a Sine Wave with a DC Offset
http://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-value-sine-wave-no-dc-offset-7.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-calculation-6.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-calculation-5.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/power-reduction-formula-4.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/sine-wave-rms-no-offset-3.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/sine-wave-2.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-definition-1.png


5/14



Figure 2

Now, lets look at a sine wave with a DC offset. This waveform is shown in Figure 2 and is described by the following function.

(8)

where with a0I noted the DC offset. Applying the RMS definition, the RMS squared can be written as:

(9)

Lets calculate the integral.

(10)

(11)

(12)

(13)

(14)

Therefore, the RMS value of a sine wave with a DC offset is given by the following expression.

(15)

The immediate verification of the validity of this expression is the RMS value of a sine wave with zero DC offset. Indeed, when a0= 0

V, the RMS level reverts back to equation (7), which is 0.707 of the sine amplitude.

Expression (15) can also be verified by comparing it with Parsevals Theorem. This theorem says that the integral of the square of a

function is equal with the integral of the squared components of its spectrum. In effect, the theorem states that the total energy of a

waveform can be found in the total energy of the waveforms Fourier components. In our case, a0is the DC level, or the frequency zero

component, and a1is the fundamental frequency. There are no other Fourier components. As such, the RMS value of a sine wave with

a DC offset as given by expression (15) is correct.
http://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-value-sine-wave-with-dc-offset-15.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-calculation-14.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-calculation-13.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-calculation-12.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-calculation-11.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-calculation-10.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/rms-calculation-9.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/sine-wave-with-DC-offset-8.pnghttp://masteringelectronicsdesign.com/wp-content/uploads/2012/02/sine-wave-with-DC-offset.png


6/14



86 people like this. Sign Upto see w hat your friends like.Like

(This article was viewed 105,295 times)

Tags: RMS, waveform

Categories: Analog Design, RMS, Waveforms

My Interview in EEWeb

Open-loop, Closed-loop and Feedback Questions and Answers

45 Comments to How to Derive the RMS Value of a Sine Wave with a DC Offset

1.Brian Coodesays:

April 6, 2012 at 1:44 pm

Helped me refresh some theory

Reply

Adrian S. Nastasesays:

June 24, 2012 at 6:17 pm

Glad to hear that. Come back soon.

Reply

vishnusays:

June 25, 2015 at 3:18 am

Sine wave having rms value =100v is superimposed with 50 v DC supply ?

Reply


June 25, 2015 at 6:16 am

You need to reformulate your question. I do not understand what is it that you are asking.

Reply

2.Davidsays:

April 18, 2012 at 11:32 am

So do True RMS multimeters read this value correctly if there is a DC offset on a sine wave or are they really AC coupled

and read the RMS value of the AC component only? If I owned a true RMS meter, I would try it myself but alas, I dont.

Reply


June 24, 2012 at 6:15 pm

You need to check the datasheet of the multimeter. Not all of them are capable of measuring the RMS value of an AC

signal riding on a DC level. I would not take that for granted, even if it says true RMS measurement. Most manufacturers

will make sure to write this capability in the multimeter feature list.

Reply

3. Tom - houston samsung repairsays:

August 2, 2012 at 9:23 pm

I was highly skilled in Math in a previous life. Ever since then, I forgot most of my teachings. After reading this article, my

memory gradually began to be refreshed. Thank you.
http://www.cpr-houstongalleria.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=6778#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=5983#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=24999#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=24988#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=6779#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=5890#respondhttp://masteringelectronicsdesign.com/open-loop-closed-loop-and-feedback-questions-and-answers/http://masteringelectronicsdesign.com/adrian-s-nastase-interview-in-eeweb/http://masteringelectronicsdesign.com/category/waveforms/http://masteringelectronicsdesign.com/category/rms/http://masteringelectronicsdesign.com/category/analog-design/http://masteringelectronicsdesign.com/tag/waveform/http://masteringelectronicsdesign.com/tag/rms/https://www.facebook.com/campaign/landing.php?campaign_id=137675572948107&partner_id=masteringelectronicsdesign.com&placement=like_plugin&extra_1=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&extra_2=IN


7/14



Reply

4. Theosays:

August 25, 2012 at 7:43 am

Thanks, correct apart from the last line! Either u-squared OR root the RHS!

Reply


August 25, 2012 at 6:44 pm

Thank you for seeing that typo. I fixed it.

Reply

5. ashishsays:

August 25, 2012 at 2:45 pm

infinite thanks sir,specially why the sine term becomes zero,I searched lot on that yours explanation is best.

Reply

6.Javed Bukharisays:

September 13, 2012 at 4:57 pm

RMS really points to the heating enregy present in any waveform. So be it Sine wave or DC voltage riding on it irrespective of

the polority of any component the final effect of all the components is governned by superposition theorm, provided the effective

bandwidth is infinite or close to it.

Reply

7.Jessie Msays:

September 20, 2012 at 4:16 am

Excellent article, sir and thank you for this website.

Reply

8.DRBsays:

October 3, 2012 at 7:20 pm

For the purposes of an actual answer, doesnt a1 need to be the peak of the non offset sinusoid, not the peak of the shifted

sinusoid(as shown in your figure 2)?

Reply


October 4, 2012 at 7:25 pm

Yes, that is the case, as figure 1 shows. Ill make sure to make it clearer on figure 2 by adding/subtracting a1 from offset.

Thank you for your comment.

Reply9.J. Husays:

November 7, 2012 at 2:14 pm

I just calculate the RMS value using integration method, by hand, immediately after I saw this title and then scroll to the bottom o

your article to check whether Ive a correct answer. But when spectrum power shows, I realize I wasted my time,

Reply


November 8, 2012 at 6:00 am

Sure, you do not need to start with the integral, unless you want to verify my calculations. It is, indeed, a waste of time.
http://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=8290#respondhttp://www.jinkuhu.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=7697#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=7688#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=7553#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=7488#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=7273#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=7276#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=7271#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=7137#respond


8/14



Just apply the formula and youre done.

Reply

10. doxsays:

December 18, 2012 at 9:59 pm

Wouldnt it be easier to explain the answer as the square-root of the sum of squares of the RMS components?

RMS of DC = DC or a0

RMS of AC = ACpk/sqrt(2) or a1/sqrt(2)

RMS of combination = sqrt(a0^2 + a1^2/2)

This approach makes more complex functions easier to address. For example, add a triangular wave with amplitude a2 riding on

this offset sine:

RMS of triangle = Peak/sqrt(3)

RMS of combo = sqrt(a0^2 + a1^2/2 + a2^2/3)

Reply


December 18, 2012 at 10:54 pm

Your comment is correct regarding the calculation of RMS values based on the square root of the sum of squares. I am

not sure that it is simpler though. In any case, this subject is part of a planned article I am writing in this series about RMScalculation. Not everybody understands the root square of the sum of squares and I plan to explain it in the near future. In

this article I showed the derivation of the RMS value starting from the definition.

Thank you for your input.

Reply

11.Musiciansays:

January 19, 2013 at 11:02 am

Hey!

I am musician and am interested how a digital DAW would read pure DC offsets RMS and peak dbs. Any ideas on this? I think

a sine with DC offset would end up being louder on the meter and with higher peak.

Reply


January 20, 2013 at 2:24 am

By DAW you mean a Digital Audio Workstation, right? From my time in the professional audio industry I know that

offsets are dreaded in this business. So, I am not sure why you would have DC offsets getting into your DAW. But, if this

is the case, DAW will digitize whatever it sees in the input, like a digital oscilloscope would. Then it will calculate the

RMS of the signal with the square root of the sum of squared samples. I did not write an article about this method for

calculating the RMS but I will in the near future. Generally, I do not think a signal with DC offset will sound louder. And

thats because a speaker does not generate sound due to DC, just a loud pop when the system is turned on.

Reply

12. anatmansays:

March 1, 2013 at 1:08 pm

why the square in u(t)^2?

Reply


March 3, 2013 at 1:14 am

The RMS value represents the signal power, so the integral has to be of the u(t)^2. Without that square, you would
http://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=11839#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=10568#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=10549#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=9865#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=9861#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=8318#respond


9/14



calculate the average of the signal. In case of a simple sine wave the average is 0. If the sine wave has a DC offset as in

this article, the average value is the DC offset.

Reply

13. Stefansays:

April 4, 2013 at 2:59 pm

Thank you.

Reply14.Danielsays:


Thanks very much, but I have one question that keeps bugging me.

Why is the RMS calculated as the sqrt of the avg of the squares as oppose to the avg of the sqrt of the squares.

In other words why use sqrt((1/n)*(x1^2+x2^2..xn^2))

Why not use (1/n)*(sqrt(x1^2)+sqrt(x2^2).sqrt(xn^2))

Reply

Adrian S. Nastasesays:November 26, 2013 at 9:29 pm

sqrt(x1^2) = x1, right? So, in effect, you want to use the signal average (1/n)(x1 + x2 ++ xn) to calculate the RMS,

which is not correct. RMS represents power. Therefore, first calculate the sum of each component power. Once the

power is calculated perform a square root of this sum to calculate the actual voltage.

Reply

Danielsays:


Ok, so if x^2 is the power of the signal and you get them mean of x^2 ie the mean of the power than why do we

than take the sqrt of the mean.

Thanks

Reply



Because the mean of xk^2 results in Volts to the power of two, which is equivalent with Watts, the units of

power. So, to bring this back to rms voltage, you need to perform the square root of the result.

Reply

15.Pradeepsays:December 8, 2013 at 9:45 am

Very convincing and clear explanation. Thank you very much!

Extending this idea, the RMS of a waveform made by summing known simple waveforms has an RMS that is the square root of

the sum of the squares of the component RMS values if the component waveforms are orthogonal.

Reply


December 9, 2013 at 6:35 am

Correct. That will be the subject of another article. Thank you for your comment.
http://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=16860#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=16827#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=16820#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=16819#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=16818#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=12999#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=11912#respond


10/14



Reply

Thomas Grooversays:

July 22, 2014 at 9:24 pm

This article is very good and another article can generalize the results illustrated by the following example with the

necessary proofs.

If two time functions x and y are absolutely uncorrelated (r[xy] = 0) then the rms value of their sum can be found in the

way so described above.

If two time functions x and y are absolutely correlated (r[xy] = 1) then the rms value of their sum can be found as the linear

sum of the two rms values of x and y.

If two time functions x and y are partially correlated (e.g. r[xy] = .5) then the rms value of their sum can be found as the

linear sum of the two rms values calculated in the two cases above divided by two for r[xy] = .5

Reply

Thomas Grooversays:

July 22, 2014 at 9:31 pm

Should add the qualification: the two time functions x and y are what we call in EE power signals, existing for

extended time.

Reply


July 23, 2014 at 8:34 pm

Thank you Thomas. Great input.

Reply

16. aravind bosesays:

January 31, 2014 at 2:04 pm

helped a lot

Reply

17.NASAsays:

August 6, 2014 at 11:53 am

Great contribution, Adrian.

Back to the the top and your clear derivation of the rms of a constant dc+sine wave. Now, can I still use equation 15 when my

dc term ao is a decaying exponential ie ao = e^(-t/Tau)? I guess yes giving a rms value that is depends on time instant t. Am I

correct?

My second question is: my sine wave is now multiplied by a decaying exponential term like ao above giving u(t) = e^(-t/T) x

sin((wt). Again my intuition tells me the rms must also reduce with time ie must be a function of time instant t but what would the

rms equation be?

Reply



From your description it looks like your signal in both cases is aperiodic. So, equation 15 does not apply. You can still

calculate the RMS if you take a window of the signal and apply the Fourier transform. Then calculate the RMS with the

square root of the sum of squares of the Fourier components.

Reply

NASAsays:

http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17467#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17460#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17004#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17386#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17354#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17353#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=16861#respond


11/14



Thanks. Admittedly, I am very rusty on these things having graduated in 1983.

However, I think both my signals are indeed periodic with a period equal to 20 ms for a frequency of 50Hz and w

= 2xPIx50. My first signal is

u1(t) = e^(-t/Tau) cos(wt), and Tau is equal to, say, 30ms, so that after about 150 ms, the decaying dc offset

vanishes and only the alternating cosine wave remains. So, after 150ms, the rms should be equal to 0.707 but for

earlier times, the DC component should have an rms value and hence my thinking that your equation 15 can still be

used.

My 2nd function u2(t) = e^(-t/Tau) cos(wt), also appears periodic and eventually decays to zero. Now, since I

have only one term, my guess is that the rms is equal to e^(-t/Tau)/sqrt(2) which makes it time -dependent but Icannot prove it.

Reply


August 9, 2014 at 10:19 pm

Since a periodic signal is the signal that repeats itself at regular intervals, both your signals are not periodic in

the strict mathematical sense. The peak in the first cycle is not at the same level as the peak in the second

cycle. It looks periodic, but it is not. Your first example is the sum between a periodic signal and a decaying

signal. The signal becomes periodic after the decaying one disappears. That is why I said that you need to

study this signal in intervals.

If you take a scope with RMS measurements capability, you will see that the RMS value varies as the

decaying signal reduces to zero. You need to calculate the RMS starting with the definition, in a chosen

window, but I agree it is complicated. So, probably it is better to use numerical computation, the same way a

digital scope will do. Here are two methods:

1. You sample the signal with a certain sampling frequency over a window of a few cycles. Then apply the

FFT on those samples. Then you calculate the RMS for that window with the square root of the sum of

squares of the Fourier components.

2. Approximation: Consider the DC signal of your first function fixed over the first cycle. The value is the DC

value at the beginning of the cycle. Calculate RMS1 for that cycle with eq. 15. Then consider the DC signal

fixed over the second cycle. The value is the DC value at the beginning of the second cycle. Calculate RMS2for that cycle with eq. 15. And so on, up to say 10 cycles. Then add them with the square root of the sum of

square. It is an approximation, but a close one to reality and it will be over a window of 10 cycles.

Same methods apply for your second example.

Reply

NASAsays:

August 10, 2014 at 10:48 am

Your suggested 2nd method gives me exactly what I need; a sufficiently accurate approximation of

each rms value for each cycle and the reduction with time of each rms value until the DC disappears.

All is crystal clear now with a bit of rust falling off my brains.

Very many thanks for your time and help.

18.pavan kumar yallasays:

September 6, 2014 at 1:54 pm

nice explanation..easily understood

Reply

19.Mikesays:
http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17545#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17469#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17468#respond


12/14




Thank you so much for this explanation Adrian. Your ability to explain these things is exceptional! I am no mathematician, so I

cant follow all your proofs, but I get the drift of the principle involved. Just one small question: does the same principle to an all-

positive sinusoidal eg, one that varies between +5 and +15 volts? By the standard definitions of AC, this would be reckoned a

DC current/voltage, and it confuses me whether or not AC Theory can be applied to a DC waveform. Or, perhaps its just a

question of definitions, and where you place your X-axis. Thanks again for this blog.

Reply

20.Mikesays:November 9, 2014 at 5:46 pm

Sorry, meant Y-axis (also omitted an apply in fourth line!)

Reply



Mike, thank you for the review.

Regarding your question, yes, it does apply. Your sine wave has a peak to peak voltage of 15-5 = 10V. So it is a sine

wave with an amplitude of 5V and it rides on top of a DC level of 10V. At the peak the value it is 10V DC plus 5V

amplitude equals 15V. At the bottom it is 10V DC minus 5V amplitude equals 5V. So, the principle is the same, and youcan apply equation 15. The RMS value is

sqrt(10^2 + (1/2) * 5^2) = 10.607V

Reply

jansays:

March 14, 2015 at 11:28 am

Hi Adrian,

You wrote:

The RMS value is sqrt(10^2 + (1/2) * 5^2)

Well, that is sqrt(100 + 12.5).

Sqrt of 112.5 is in my humble opion 10.60660 V.Right??

I can not see how you arrive at 35.35V

Also, a VRMS will never be more that the maximum Voltage value of the signal; that should set off an alarm!

Regards

Jan

Reply


March 15, 2015 at 6:20 pm

Jan, thank you for pointing this typo out. I made the correction.

Reply

21.sandip sherchansays:

May 13, 2016 at 3:11 pm

thank you

Reply

Leave a Comment

Name (required)
http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=35314#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=21940#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=21918#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17694#respondhttp://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17692#respondhttp://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/?replytocom=17691#respond


13/14



Mail (will not be published) (required)

Website

Submit Comment

Search

Like this blog

1.2k people like this. Sign

Upto see w hat your

friendslike.

Like

Recommend this blog

Tw eet

Home

About me

Contact

Why this website?

It's an Analog World by Design

How to Apply Thevenins Theorem Part 2. Nested Thevenin Sources Method

Recent Posts

Why is the Op Amp Gain-Bandwidth Product Constant?

How to Calculate the RMS Value of an Arbitrary Waveform

Design a Unipolar to Bipolar Converter the Easy Way with Microsoft Mathematics

Tenma 72-7745 Multimeter Review

Open-loop, Closed-loop and Feedback Questions and Answers


My Interview in EEWeb

Most Popular

How to Derive the RMS Value of Pulse and Square Waveforms


How to Derive the RMS Value of a Triangle Waveform
http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-triangle-waveform/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-triangle-waveform/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-pulse-and-square-waveforms/http://masteringelectronicsdesign.com/adrian-s-nastase-interview-in-eeweb/http://masteringelectronicsdesign.com/how-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset/http://masteringelectronicsdesign.com/open-loop-closed-loop-and-feedback-questions-and-answers/http://masteringelectronicsdesign.com/tenma-72-7745-multimeter-review/http://masteringelectronicsdesign.com/design-a-unipolar-to-bipolar-converter-the-easy-way-with-microsoft-mathematics/http://masteringelectronicsdesign.com/how-to-calculate-the-rms-value-of-an-arbitrary-waveform/http://masteringelectronicsdesign.com/why-is-the-op-amp-gain-bandwidth-product-constant/http://masteringelectronicsdesign.com/how-to-apply-thevenins-theorem-part-2-nested-thevenin-sources-method/http://masteringelectronicsdesign.com/it-s-an-analog-world-by-design/http://masteringelectronicsdesign.com/why-this-website/http://masteringelectronicsdesign.com/contact-page/http://masteringelectronicsdesign.com/about-me/http://masteringelectronicsdesign.com/https://twitter.com/intent/tweet?original_referer=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&ref_src=twsrc%5Etfw&text=MasteringElectronicsDesign.com%20%3A%20How%20to%20Derive%20the%20RMS%20Value%20of%20a%20Sine%20Wave%20with%20a%20DC%20Offset&tw_p=tweetbutton&url=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2Fhttps://www.facebook.com/campaign/landing.php?campaign_id=137675572948107&partner_id=masteringelectronicsdesign.com&placement=like_plugin&extra_1=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fhow-to-derive-the-rms-value-of-a-sine-wave-with-a-dc-offset%2F&extra_2=INhttp://www.pinterest.com/pin/create/button/?url=http%3A%2F%2FMasteringElectronicsDesign.com&media=http%3A%2F%2Fmasteringelectronicsdesign.com%2Fwp-content%2Fimages%2FPinit-MasteringElectronicsDesign_com.png&description=Mastering%20Electronics%20Design


14/14


An Op Amp Gain Bandwidth Product

How to Derive the Instrumentation Amplifier Transfer

The Transfer Function of the Non-Inverting Summing Amplifier

An ADC and DAC Least Significant Bit (LSB)

How to Derive the Differential Amplifier Transfer Function

How to Derive the Summing Amplifier Transfer Function

How to Derive the Inverting Amplifier Transfer Function

Popular posts by Top 10 plugin

Categories

Analog Design

Calculators

Differential Amplifier

Education

Electronic Circuits Examples

Mixed-Signal Design

Operational Amplifier Formulas

Opinion

Power Supply

RMSSumming Amplifier

Superposition Theorem

Thevenin's Theorem

Transistor Circuits

Waveforms

Recent Comments

Adrian S. Nastaseon Design a Bipolar to Unipolar Converter to Drive an ADC

R19 on Design a Bipolar to Unipolar Converter to Drive an ADC

Adrian S. Nastaseon The Non-Inverting Amplifier Output ResistanceAdrian S. Nastaseon Design a Bipolar to Unipolar Converter to Drive an ADC

chia on The Non-Inverting Amplifier Output Resistance

Adrian S. Nastaseon How to Derive the Instrumentation Amplifier Transfer Function

Adrian S. Nastaseon The Differential Amplifier Common-Mode Error Part 2

Adrian S. Nastaseon Design a Unipolar to Bipolar Converter for a Unipolar Voltage Output DAC

Ricky on The Differential Amplifier Common-Mode Error Part 2

Ricky on How to Derive the Differential Amplifier Transfer Function

RSS (Entries)- RSS (Comments)- CONTACT- DISCLAIMER- PRIVACY POLICY

Copyright 2009-2016 Adrian S. Nastase. All Rights Reserved.
http://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/privacy-policy/http://masteringelectronicsdesign.com/disclaimer/http://masteringelectronicsdesign.com/contact-page/http://masteringelectronicsdesign.com/comments/feed/http://masteringelectronicsdesign.com/?feed=rss2http://www.webutation.net/go/review/masteringelectronicsdesign.comhttp://masteringelectronicsdesign.com/the-differential-amplifier-transfer-function/#comment-35363http://masteringelectronicsdesign.com/the-differential-amplifier-common-mode-error-part-2/#comment-35378http://masteringelectronicsdesign.com/design-a-unipolar-to-bipolar-converter-for-a-unipolar-voltage-output-dac/#comment-35408http://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/the-differential-amplifier-common-mode-error-part-2/#comment-35433http://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/how-to-derive-the-instrumentation-amplifier-transfer-function/#comment-35435http://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/the-non-inverting-amplifier-output-resistance/#comment-35460http://masteringelectronicsdesign.com/design-a-bipolar-to-unipolar-converter/#comment-36281http://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/the-non-inverting-amplifier-output-resistance/#comment-36010http://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/design-a-bipolar-to-unipolar-converter/#comment-36182http://masteringelectronicsdesign.com/design-a-bipolar-to-unipolar-converter/#comment-36304http://masteringelectronicsdesign.com/http://masteringelectronicsdesign.com/category/waveforms/http://masteringelectronicsdesign.com/category/transistor-circuits/http://masteringelectronicsdesign.com/category/thevenins-theorem/http://masteringelectronicsdesign.com/category/superposition-theorem/http://masteringelectronicsdesign.com/category/summing-amplifier/http://masteringelectronicsdesign.com/category/rms/http://masteringelectronicsdesign.com/category/power-supply/http://masteringelectronicsdesign.com/category/opinion/http://masteringelectronicsdesign.com/category/operational-amplifier-formulas/http://masteringelectronicsdesign.com/category/mixed-signal-design/http://masteringelectronicsdesign.com/category/electronic-circuits-examples/http://masteringelectronicsdesign.com/category/education/http://masteringelectronicsdesign.com/category/differential-amplifier/http://masteringelectronicsdesign.com/category/calculators/http://masteringelectronicsdesign.com/category/analog-design/https://webberzone.com/plugins/top-10/http://masteringelectronicsdesign.com/how-to-derive-the-inverting-amplifier-transfer-function/http://masteringelectronicsdesign.com/how-to-derive-the-summing-amplifier-transfer-function/http://masteringelectronicsdesign.com/the-differential-amplifier-transfer-function/http://masteringelectronicsdesign.com/an-adc-and-dac-least-significant-bit-lsb/http://masteringelectronicsdesign.com/the-transfer-function-of-the-summing-amplifier-with-n-input-signals/http://masteringelectronicsdesign.com/how-to-derive-the-instrumentation-amplifier-transfer-function/http://masteringelectronicsdesign.com/an-op-amp-gain-bandwidth-product/

Documents

Mastering Electronics Design